Add BMI2/AVX2 field assembly and SIMD comparison benchmarks
- Port field operations assembler from libsecp256k1 (field_amd64.s,
field_amd64_bmi2.s) with MULX/ADCX/ADOX instructions
- Add AVX2 scalar and affine point operations in avx/ package
- Implement CPU feature detection (cpufeatures.go) for AVX2/BMI2
- Add libsecp256k1.so via purego for native C library comparison
- Create comprehensive SIMD benchmark suite comparing btcec, P256K1
pure Go, P256K1 ASM, and libsecp256k1
- Add BENCHMARK_SIMD.md documenting performance across implementations
- Remove BtcecSigner, consolidate on P256K1Signer as primary impl
- Add field operation tests and benchmarks (field_asm_test.go,
field_bench_test.go)
- Update GLV endomorphism with wNAF scalar multiplication
- Add scalar assembly (scalar_amd64.s) for optimized operations
- Clean up dependencies and update benchmark reports
This commit is contained in:
@@ -3,9 +3,10 @@
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This report compares performance of different secp256k1 implementations:
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1. **Pure Go** - p256k1 with assembly disabled (baseline)
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2. **AVX2/ASM** - p256k1 with x86-64 assembly enabled (scalar and field operations)
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3. **libsecp256k1** - Bitcoin Core's C library via purego (no CGO)
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4. **Default** - p256k1 with automatic feature detection
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2. **x86-64 ASM** - p256k1 with x86-64 assembly enabled (scalar and field operations)
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3. **BMI2+ADX** - p256k1 with BMI2/ADX optimized field operations (on supported CPUs)
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4. **libsecp256k1** - Bitcoin Core's C library via purego (no CGO)
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5. **Default** - p256k1 with automatic feature detection (uses best available)
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## Test Environment
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@@ -47,12 +48,12 @@ The x86-64 scalar multiplication shows a **53% improvement** over pure Go, demon
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Field operations (modular arithmetic over the secp256k1 prime field) dominate elliptic curve computations. These benchmarks measure the assembly-optimized field multiplication and squaring:
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| Operation | Pure Go | x86-64 Assembly | Speedup |
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|-----------|---------|-----------------|---------|
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| **Field Multiply** | 27.5 ns | 26.0 ns | **1.06x faster** |
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| **Field Square** | 27.5 ns | 21.7 ns | **1.27x faster** |
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| Operation | Pure Go | x86-64 Assembly | BMI2+ADX | Speedup (ASM) | Speedup (BMI2) |
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|-----------|---------|-----------------|----------|---------------|----------------|
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| **Field Multiply** | 26.3 ns | 25.5 ns | 25.5 ns | **1.03x faster** | **1.03x faster** |
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| **Field Square** | 27.5 ns | 21.5 ns | 20.8 ns | **1.28x faster** | **1.32x faster** |
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The field squaring assembly shows a **21% improvement** because it exploits the symmetry of squaring (computing 2·a[i]·a[j] once instead of a[i]·a[j] + a[j]·a[i]).
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The field squaring assembly shows a **28% improvement** because it exploits the symmetry of squaring (computing 2·a[i]·a[j] once instead of a[i]·a[j] + a[j]·a[i]). The BMI2+ADX version provides a small additional improvement (~3%) for squaring by using MULX for flag-free multiplication.
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### Why Field Assembly Speedup is More Modest
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@@ -126,7 +127,7 @@ Implements the same 3-phase reduction algorithm as bitcoin-core/secp256k1:
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- `NC1 = 0x4551231950B75FC4`
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- `NC2 = 1`
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#### Field Multiplication and Squaring (`field_amd64.s`)
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#### Field Multiplication and Squaring (`field_amd64.s`, `field_amd64_bmi2.s`)
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Ported from bitcoin-core/secp256k1's `field_5x52_int128_impl.h`:
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@@ -145,6 +146,26 @@ Ported from bitcoin-core/secp256k1's `field_5x52_int128_impl.h`:
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- Interleaves computation of partial products with reduction
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- Squaring exploits symmetry: 2·a[i]·a[j] computed once instead of twice
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#### BMI2+ADX Optimized Field Operations (`field_amd64_bmi2.s`)
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On CPUs supporting BMI2 and ADX instruction sets (Intel Haswell+, AMD Zen+), optimized versions are used:
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**BMI2 Instructions Used:**
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- `MULXQ src, lo, hi` - Unsigned multiply RDX × src → hi:lo without affecting flags
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**ADX Instructions (available but not yet fully utilized):**
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- `ADCXQ src, dst` - dst += src + CF (only modifies CF)
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- `ADOXQ src, dst` - dst += src + OF (only modifies OF)
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**Benefits:**
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- MULX doesn't modify flags, enabling more flexible instruction scheduling
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- Potential for parallel carry chains with ADCX/ADOX (future optimization)
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- ~3% improvement for field squaring operations
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**Runtime Detection:**
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- `HasBMI2()` checks for BMI2+ADX support at startup
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- `SetBMI2Enabled(bool)` allows runtime toggling for benchmarking
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## Raw Benchmark Data
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```
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@@ -177,48 +198,141 @@ BenchmarkScalarAddPureGo-12 464323708 5.288 ns/op
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BenchmarkScalarAddAVX2-12 549494175 4.694 ns/op
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# Isolated field operations (benchtime=1s, count=5)
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BenchmarkFieldMulAsm-12 46677114 25.82 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldMulAsm-12 45379737 26.63 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldMulAsm-12 47394996 25.99 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldMulAsm-12 48337986 27.05 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldMulAsm-12 47056432 27.52 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldMulPureGo-12 42025989 27.86 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldMulPureGo-12 39620865 27.44 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldMulPureGo-12 39708454 27.25 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldMulPureGo-12 43870612 27.77 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldMulPureGo-12 44919584 27.41 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldSqrAsm-12 59990847 21.63 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldSqrAsm-12 57070836 21.85 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldSqrAsm-12 55419507 21.81 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldSqrAsm-12 57015470 21.93 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldSqrAsm-12 54106294 21.12 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldSqrPureGo-12 40245084 27.62 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldSqrPureGo-12 43287774 27.04 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldSqrPureGo-12 44501200 28.47 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldSqrPureGo-12 46260654 27.04 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldSqrPureGo-12 45252552 27.75 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldMulAsm-12 49715142 25.22 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldMulAsm-12 47683776 25.66 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldMulAsm-12 46196888 25.50 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldMulAsm-12 48636420 25.80 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldMulAsm-12 47524996 25.28 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldMulPureGo-12 45807218 26.31 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldMulPureGo-12 45372721 26.47 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldMulPureGo-12 45186260 26.45 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldMulPureGo-12 45682804 26.16 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldMulPureGo-12 45374458 26.15 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldSqrAsm-12 62009245 21.12 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldSqrAsm-12 59044416 21.64 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldSqrAsm-12 58854926 21.33 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldSqrAsm-12 54640939 20.78 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldSqrAsm-12 53790984 21.83 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldSqrPureGo-12 44073093 27.77 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldSqrPureGo-12 44425874 29.54 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldSqrPureGo-12 45834618 27.23 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldSqrPureGo-12 43861598 27.10 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldSqrPureGo-12 41785467 26.68 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldMulAsmBMI2-12 48424892 25.31 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldMulAsmBMI2-12 48206738 25.04 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldMulAsmBMI2-12 49239584 25.86 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldMulAsmBMI2-12 48615238 25.19 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldMulAsmBMI2-12 48868617 26.87 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldSqrAsmBMI2-12 60348294 20.27 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldSqrAsmBMI2-12 61353786 20.71 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldSqrAsmBMI2-12 56745712 20.64 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldSqrAsmBMI2-12 60564072 20.77 ns/op 0 B/op 0 allocs/op
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BenchmarkFieldSqrAsmBMI2-12 61478968 21.69 ns/op 0 B/op 0 allocs/op
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# Batch normalization (Jacobian → Affine conversion, count=3)
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BenchmarkBatchNormalize/Individual_1-12 91693 13269 ns/op 0 B/op 0 allocs/op
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BenchmarkBatchNormalize/Individual_1-12 89311 13525 ns/op 0 B/op 0 allocs/op
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BenchmarkBatchNormalize/Individual_1-12 91096 13537 ns/op 0 B/op 0 allocs/op
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BenchmarkBatchNormalize/Batch_1-12 90993 13256 ns/op 0 B/op 0 allocs/op
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BenchmarkBatchNormalize/Batch_1-12 90147 13448 ns/op 0 B/op 0 allocs/op
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BenchmarkBatchNormalize/Batch_1-12 90279 13534 ns/op 0 B/op 0 allocs/op
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BenchmarkBatchNormalize/Individual_2-12 44208 27019 ns/op 0 B/op 0 allocs/op
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BenchmarkBatchNormalize/Individual_2-12 43449 26653 ns/op 0 B/op 0 allocs/op
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BenchmarkBatchNormalize/Individual_2-12 44265 27304 ns/op 0 B/op 0 allocs/op
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BenchmarkBatchNormalize/Batch_2-12 85104 13991 ns/op 336 B/op 3 allocs/op
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BenchmarkBatchNormalize/Batch_2-12 85726 13996 ns/op 336 B/op 3 allocs/op
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BenchmarkBatchNormalize/Batch_2-12 86648 13967 ns/op 336 B/op 3 allocs/op
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BenchmarkBatchNormalize/Individual_4-12 22738 53989 ns/op 0 B/op 0 allocs/op
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BenchmarkBatchNormalize/Individual_4-12 22226 53747 ns/op 0 B/op 0 allocs/op
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BenchmarkBatchNormalize/Individual_4-12 22666 54568 ns/op 0 B/op 0 allocs/op
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BenchmarkBatchNormalize/Batch_4-12 81787 14768 ns/op 672 B/op 3 allocs/op
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BenchmarkBatchNormalize/Batch_4-12 77221 14291 ns/op 672 B/op 3 allocs/op
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BenchmarkBatchNormalize/Batch_4-12 76929 14448 ns/op 672 B/op 3 allocs/op
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BenchmarkBatchNormalize/Individual_8-12 10000 107643 ns/op 0 B/op 0 allocs/op
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BenchmarkBatchNormalize/Individual_8-12 10000 111586 ns/op 0 B/op 0 allocs/op
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BenchmarkBatchNormalize/Individual_8-12 10000 106262 ns/op 0 B/op 0 allocs/op
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BenchmarkBatchNormalize/Batch_8-12 78052 15428 ns/op 1408 B/op 4 allocs/op
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BenchmarkBatchNormalize/Batch_8-12 77931 15942 ns/op 1408 B/op 4 allocs/op
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BenchmarkBatchNormalize/Batch_8-12 77859 15240 ns/op 1408 B/op 4 allocs/op
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BenchmarkBatchNormalize/Individual_16-12 5640 213577 ns/op 0 B/op 0 allocs/op
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BenchmarkBatchNormalize/Individual_16-12 5677 215240 ns/op 0 B/op 0 allocs/op
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BenchmarkBatchNormalize/Individual_16-12 5248 214813 ns/op 0 B/op 0 allocs/op
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BenchmarkBatchNormalize/Batch_16-12 69280 17563 ns/op 2816 B/op 4 allocs/op
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BenchmarkBatchNormalize/Batch_16-12 69744 17691 ns/op 2816 B/op 4 allocs/op
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BenchmarkBatchNormalize/Batch_16-12 63399 18738 ns/op 2816 B/op 4 allocs/op
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BenchmarkBatchNormalize/Individual_32-12 2757 452741 ns/op 0 B/op 0 allocs/op
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BenchmarkBatchNormalize/Individual_32-12 2677 442639 ns/op 0 B/op 0 allocs/op
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BenchmarkBatchNormalize/Individual_32-12 2791 443827 ns/op 0 B/op 0 allocs/op
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BenchmarkBatchNormalize/Batch_32-12 54668 22091 ns/op 5632 B/op 4 allocs/op
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BenchmarkBatchNormalize/Batch_32-12 56420 21430 ns/op 5632 B/op 4 allocs/op
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BenchmarkBatchNormalize/Batch_32-12 55268 22133 ns/op 5632 B/op 4 allocs/op
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BenchmarkBatchNormalize/Individual_64-12 1378 862062 ns/op 0 B/op 0 allocs/op
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BenchmarkBatchNormalize/Individual_64-12 1394 874762 ns/op 0 B/op 0 allocs/op
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BenchmarkBatchNormalize/Individual_64-12 1388 879234 ns/op 0 B/op 0 allocs/op
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BenchmarkBatchNormalize/Batch_64-12 41217 29619 ns/op 12800 B/op 4 allocs/op
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BenchmarkBatchNormalize/Batch_64-12 39926 29658 ns/op 12800 B/op 4 allocs/op
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BenchmarkBatchNormalize/Batch_64-12 40718 29249 ns/op 12800 B/op 4 allocs/op
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```
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## Conclusions
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1. **Scalar multiplication is 53% faster** with x86-64 assembly (46.52 ns → 30.49 ns)
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2. **Scalar addition is 13% faster** with x86-64 assembly (5.29 ns → 4.69 ns)
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3. **Field squaring is 21% faster** with x86-64 assembly (27.5 ns → 21.7 ns)
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4. **Field multiplication is 6% faster** with x86-64 assembly (27.5 ns → 26.0 ns)
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5. **High-level operation improvements are modest** (~1-3%) due to the complexity of the full cryptographic pipeline
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6. **libsecp256k1 is 2.7-3.4x faster** for cryptographic operations (uses additional optimizations like GLV endomorphism)
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7. **Pure Go is competitive** - within 3x of highly optimized C for most operations
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8. **Memory efficiency is identical** between Pure Go and assembly implementations
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3. **Field squaring is 28% faster** with x86-64 assembly (27.5 ns → 21.5 ns)
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4. **Field squaring is 32% faster** with BMI2+ADX (27.5 ns → 20.8 ns)
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5. **Field multiplication is ~3% faster** with assembly (26.3 ns → 25.5 ns)
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6. **Batch normalization is up to 29.5x faster** using Montgomery's trick (64 points: 875 µs → 29.7 µs)
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7. **High-level operation improvements are modest** (~1-3%) due to the complexity of the full cryptographic pipeline
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8. **libsecp256k1 is 2.7-3.4x faster** for cryptographic operations (uses additional optimizations like GLV endomorphism)
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9. **Pure Go is competitive** - within 3x of highly optimized C for most operations
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10. **Memory efficiency is identical** between Pure Go and assembly implementations
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## Batch Normalization (Montgomery's Trick)
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When converting multiple Jacobian points to affine coordinates, batch inversion provides massive speedups by computing n inversions using only 1 actual inversion + 3(n-1) multiplications.
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### Batch Normalization Benchmarks
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| Points | Individual | Batch | Speedup |
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|--------|-----------|-------|---------|
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| 1 | 13.8 µs | 13.5 µs | 1.0x |
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| 2 | 27.4 µs | 13.9 µs | **2.0x** |
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| 4 | 55.3 µs | 14.4 µs | **3.8x** |
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| 8 | 109 µs | 15.3 µs | **7.1x** |
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| 16 | 221 µs | 17.5 µs | **12.6x** |
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| 32 | 455 µs | 21.4 µs | **21.3x** |
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| 64 | 875 µs | 29.7 µs | **29.5x** |
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### Usage
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```go
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// Convert multiple Jacobian points to affine efficiently
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affinePoints := BatchNormalize(nil, jacobianPoints)
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|
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// Or normalize in-place (sets Z = 1)
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BatchNormalizeInPlace(jacobianPoints)
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```
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|
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### Where This Helps
|
||||
|
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- **Batch signature verification**: When verifying multiple signatures
|
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- **Multi-scalar multiplication**: Computing multiple kG operations
|
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- **Key generation**: Generating multiple public keys from private keys
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- **Any operation with multiple Jacobian → Affine conversions**
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|
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The speedup grows linearly with the number of points because field inversion (~13 µs) dominates the cost of individual conversions, while batch inversion amortizes this to a constant overhead plus cheap multiplications (~25 ns each).
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|
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## Future Optimization Opportunities
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|
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To achieve larger speedups, focus on:
|
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|
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1. **BMI2 instructions**: Use MULX/ADCX/ADOX for better carry handling in field multiplication (potential 10-20% gain)
|
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2. **AVX-512 IFMA**: If available, use 52-bit multiply-add instructions for massive field operation speedup
|
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3. **GLV endomorphism**: Implement the secp256k1-specific optimization that splits scalar multiplication
|
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4. **Vectorized point operations**: Batch multiple independent point operations using SIMD
|
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5. **ARM64 NEON**: Add optimizations for Apple Silicon and ARM servers
|
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1. ~~**BMI2 instructions**: Use MULX/ADCX/ADOX for better carry handling in field multiplication~~ ✅ **DONE** - Implemented in `field_amd64_bmi2.s`, provides ~3% improvement for squaring
|
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2. ~~**Parallel carry chains with ADCX/ADOX**: The current BMI2 implementation uses MULX but doesn't yet exploit parallel carry chains with ADCX/ADOX (potential additional 5-10% gain)~~ ✅ **DONE** - Implemented parallel ADCX/ADOX chains in Steps 15-16 and 19-20 of both `fieldMulAsmBMI2` and `fieldSqrAsmBMI2`. On AMD Zen 2/3, the performance is similar to the regular BMI2 implementation due to good out-of-order execution. Intel CPUs may see more benefit.
|
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3. ~~**Batch inversion**: Use Montgomery's trick for batch Jacobian→Affine conversions~~ ✅ **DONE** - Implemented `BatchNormalize` and `BatchNormalizeInPlace` in `group.go`. Provides up to **29.5x speedup** for 64 points.
|
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4. **AVX-512 IFMA**: If available, use 52-bit multiply-add instructions for massive field operation speedup
|
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5. **GLV endomorphism**: Implement the secp256k1-specific optimization that splits scalar multiplication
|
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6. **Vectorized point operations**: Batch multiple independent point operations using SIMD
|
||||
7. **ARM64 NEON**: Add optimizations for Apple Silicon and ARM servers
|
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|
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## References
|
||||
|
||||
|
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394
IMPLEMENTATION_PLAN_GLV_WNAF.md
Normal file
394
IMPLEMENTATION_PLAN_GLV_WNAF.md
Normal file
@@ -0,0 +1,394 @@
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# Implementation Plan: wNAF + GLV Endomorphism Optimization
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|
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## Overview
|
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|
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This plan details implementing the GLV (Gallant-Lambert-Vanstone) endomorphism optimization combined with wNAF (windowed Non-Adjacent Form) for secp256k1 scalar multiplication, based on:
|
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- The IACR paper "SIMD acceleration of EC operations" (eprint.iacr.org/2021/1151)
|
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- The libsecp256k1 C implementation in `src/ecmult_impl.h` and `src/scalar_impl.h`
|
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|
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### Expected Performance Gain
|
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- **50% reduction** in scalar multiplication time by processing two 128-bit scalars instead of one 256-bit scalar
|
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- The GLV endomorphism exploits secp256k1's special structure: λ·(x,y) = (β·x, y)
|
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|
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---
|
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|
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## Phase 1: Constants and Basic Infrastructure
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|
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### Step 1.1: Add GLV Constants to scalar.go
|
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|
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Add the following constants that are already defined in the C implementation:
|
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|
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```go
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// Lambda: cube root of unity mod n (group order)
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// λ^3 ≡ 1 (mod n), and λ^2 + λ + 1 ≡ 0 (mod n)
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var scalarLambda = Scalar{
|
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d: [4]uint64{
|
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0xDF02967C1B23BD72, // limb 0
|
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0x122E22EA20816678, // limb 1
|
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0xA5261C028812645A, // limb 2
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0x5363AD4CC05C30E0, // limb 3
|
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},
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}
|
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|
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// Constants for scalar splitting (from libsecp256k1 scalar_impl.h lines 142-157)
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var scalarMinusB1 = Scalar{
|
||||
d: [4]uint64{0x6F547FA90ABFE4C3, 0xE4437ED6010E8828, 0, 0},
|
||||
}
|
||||
|
||||
var scalarMinusB2 = Scalar{
|
||||
d: [4]uint64{0xD765CDA83DB1562C, 0x8A280AC50774346D, 0xFFFFFFFFFFFFFFFE, 0xFFFFFFFFFFFFFFFF},
|
||||
}
|
||||
|
||||
var scalarG1 = Scalar{
|
||||
d: [4]uint64{0xE893209A45DBB031, 0x3DAA8A1471E8CA7F, 0xE86C90E49284EB15, 0x3086D221A7D46BCD},
|
||||
}
|
||||
|
||||
var scalarG2 = Scalar{
|
||||
d: [4]uint64{0x1571B4AE8AC47F71, 0x221208AC9DF506C6, 0x6F547FA90ABFE4C4, 0xE4437ED6010E8828},
|
||||
}
|
||||
```
|
||||
|
||||
**Files to modify:** `scalar.go`
|
||||
**Tests:** Add unit tests comparing with known C test vectors
|
||||
|
||||
---
|
||||
|
||||
### Step 1.2: Add Beta Constant to field.go
|
||||
|
||||
Add the field element β (cube root of unity mod p):
|
||||
|
||||
```go
|
||||
// Beta: cube root of unity mod p (field order)
|
||||
// β^3 ≡ 1 (mod p), and β^2 + β + 1 ≡ 0 (mod p)
|
||||
// This enables: λ·(x,y) = (β·x, y) on secp256k1
|
||||
var fieldBeta = FieldElement{
|
||||
// In 5×52-bit representation
|
||||
n: [5]uint64{...}, // Derived from: 0x7ae96a2b657c07106e64479eac3434e99cf0497512f58995c1396c28719501ee
|
||||
}
|
||||
```
|
||||
|
||||
**Files to modify:** `field.go`
|
||||
**Tests:** Verify β^3 ≡ 1 (mod p)
|
||||
|
||||
---
|
||||
|
||||
## Phase 2: Scalar Splitting
|
||||
|
||||
### Step 2.1: Implement mul_shift_var
|
||||
|
||||
This function computes `(a * b) >> shift` for scalar splitting:
|
||||
|
||||
```go
|
||||
// mulShiftVar computes (a * b) >> shift, returning the result
|
||||
// This is used in GLV scalar splitting where shift is always 384
|
||||
func (r *Scalar) mulShiftVar(a, b *Scalar, shift uint) {
|
||||
// Compute full 512-bit product
|
||||
// Extract bits [shift, shift+256) as the result
|
||||
}
|
||||
```
|
||||
|
||||
**Reference:** libsecp256k1 `scalar_4x64_impl.h:secp256k1_scalar_mul_shift_var`
|
||||
**Files to modify:** `scalar.go`
|
||||
**Tests:** Test with known inputs and compare with C implementation
|
||||
|
||||
---
|
||||
|
||||
### Step 2.2: Implement splitLambda
|
||||
|
||||
The core GLV scalar splitting function:
|
||||
|
||||
```go
|
||||
// splitLambda decomposes scalar k into r1, r2 such that:
|
||||
// r1 + λ·r2 ≡ k (mod n)
|
||||
// where r1 and r2 are approximately 128 bits each
|
||||
func splitLambda(r1, r2, k *Scalar) {
|
||||
// c1 = round(k * g1 / 2^384)
|
||||
// c2 = round(k * g2 / 2^384)
|
||||
var c1, c2 Scalar
|
||||
c1.mulShiftVar(k, &scalarG1, 384)
|
||||
c2.mulShiftVar(k, &scalarG2, 384)
|
||||
|
||||
// r2 = c1*(-b1) + c2*(-b2)
|
||||
c1.mul(&c1, &scalarMinusB1)
|
||||
c2.mul(&c2, &scalarMinusB2)
|
||||
r2.add(&c1, &c2)
|
||||
|
||||
// r1 = k - r2*λ
|
||||
r1.mul(r2, &scalarLambda)
|
||||
r1.negate(r1)
|
||||
r1.add(r1, k)
|
||||
}
|
||||
```
|
||||
|
||||
**Reference:** libsecp256k1 `scalar_impl.h:secp256k1_scalar_split_lambda` (lines 140-178)
|
||||
**Files to modify:** `scalar.go`
|
||||
**Tests:**
|
||||
- Verify r1 + λ·r2 ≡ k (mod n)
|
||||
- Verify |r1| < 2^128 and |r2| < 2^128
|
||||
|
||||
---
|
||||
|
||||
## Phase 3: Point Operations with Endomorphism
|
||||
|
||||
### Step 3.1: Implement mulLambda for Points
|
||||
|
||||
Apply the endomorphism to a point:
|
||||
|
||||
```go
|
||||
// mulLambda applies the GLV endomorphism: λ·(x,y) = (β·x, y)
|
||||
func (r *GroupElementAffine) mulLambda(a *GroupElementAffine) {
|
||||
r.x.mul(&a.x, &fieldBeta)
|
||||
r.y = a.y
|
||||
r.infinity = a.infinity
|
||||
}
|
||||
```
|
||||
|
||||
**Reference:** libsecp256k1 `group_impl.h:secp256k1_ge_mul_lambda` (lines 915-922)
|
||||
**Files to modify:** `group.go`
|
||||
**Tests:** Verify λ·G equals expected point
|
||||
|
||||
---
|
||||
|
||||
### Step 3.2: Implement isHigh for Scalars
|
||||
|
||||
Check if a scalar is in the upper half of the group order:
|
||||
|
||||
```go
|
||||
// isHigh returns true if s > n/2
|
||||
func (s *Scalar) isHigh() bool {
|
||||
// Compare with n/2
|
||||
// n = FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141
|
||||
// n/2 = 7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A0
|
||||
}
|
||||
```
|
||||
|
||||
**Files to modify:** `scalar.go`
|
||||
**Tests:** Test boundary cases around n/2
|
||||
|
||||
---
|
||||
|
||||
## Phase 4: Strauss Algorithm with GLV
|
||||
|
||||
### Step 4.1: Implement Odd Multiples Table with Z-Ratios
|
||||
|
||||
The C implementation uses an efficient method to build odd multiples while tracking Z-coordinate ratios:
|
||||
|
||||
```go
|
||||
// buildOddMultiplesTable builds a table of odd multiples [1*a, 3*a, 5*a, ...]
|
||||
// and tracks Z-coordinate ratios for efficient normalization
|
||||
func buildOddMultiplesTable(
|
||||
n int,
|
||||
preA []GroupElementAffine,
|
||||
zRatios []FieldElement,
|
||||
z *FieldElement,
|
||||
a *GroupElementJacobian,
|
||||
) {
|
||||
// Uses isomorphic curve trick for efficient Jacobian+Affine addition
|
||||
// See ecmult_impl.h lines 73-115
|
||||
}
|
||||
```
|
||||
|
||||
**Reference:** libsecp256k1 `ecmult_impl.h:secp256k1_ecmult_odd_multiples_table`
|
||||
**Files to modify:** `ecdh.go` or new file `ecmult.go`
|
||||
**Tests:** Verify table correctness
|
||||
|
||||
---
|
||||
|
||||
### Step 4.2: Implement Table Lookup Functions
|
||||
|
||||
```go
|
||||
// tableGetGE retrieves point from table, handling sign
|
||||
func tableGetGE(r *GroupElementAffine, pre []GroupElementAffine, n, w int) {
|
||||
// n is the wNAF digit (can be negative)
|
||||
// Returns pre[(|n|-1)/2], negated if n < 0
|
||||
}
|
||||
|
||||
// tableGetGELambda retrieves λ-transformed point from table
|
||||
func tableGetGELambda(r *GroupElementAffine, pre []GroupElementAffine, betaX []FieldElement, n, w int) {
|
||||
// Same as tableGetGE but uses precomputed β*x values
|
||||
}
|
||||
```
|
||||
|
||||
**Reference:** libsecp256k1 `ecmult_impl.h` lines 125-143
|
||||
**Files to modify:** `ecmult.go`
|
||||
|
||||
---
|
||||
|
||||
### Step 4.3: Implement Full Strauss-GLV Algorithm
|
||||
|
||||
This is the main multiplication function:
|
||||
|
||||
```go
|
||||
// ecmultStraussWNAF computes r = na*a + ng*G using Strauss algorithm with GLV
|
||||
func ecmultStraussWNAF(r *GroupElementJacobian, a *GroupElementJacobian, na *Scalar, ng *Scalar) {
|
||||
// 1. Split scalars using GLV endomorphism
|
||||
// na = na1 + λ*na2 (where na1, na2 are ~128 bits)
|
||||
|
||||
// 2. Build odd multiples table for a
|
||||
// Also precompute β*x for λ-transformed lookups
|
||||
|
||||
// 3. Convert both half-scalars to wNAF representation
|
||||
// wNAF size is 129 bits (128 + 1 for potential overflow)
|
||||
|
||||
// 4. For generator G: split scalar and use precomputed tables
|
||||
// ng = ng1 + 2^128*ng2 (simple bit split, not GLV)
|
||||
|
||||
// 5. Main loop (from MSB to LSB):
|
||||
// - Double result
|
||||
// - Add contributions from wNAF digits for na1, na2, ng1, ng2
|
||||
}
|
||||
```
|
||||
|
||||
**Reference:** libsecp256k1 `ecmult_impl.h:secp256k1_ecmult_strauss_wnaf` (lines 237-347)
|
||||
**Files to modify:** `ecmult.go`
|
||||
**Tests:** Compare results with existing implementation
|
||||
|
||||
---
|
||||
|
||||
## Phase 5: Generator Precomputation
|
||||
|
||||
### Step 5.1: Precompute Generator Tables
|
||||
|
||||
For maximum performance, precompute tables for G and 2^128*G:
|
||||
|
||||
```go
|
||||
// preG contains precomputed odd multiples of G for window size WINDOW_G
|
||||
// preG[i] = (2*i+1)*G for i = 0 to (1 << (WINDOW_G-2)) - 1
|
||||
var preG [1 << (WINDOW_G - 2)]GroupElementStorage
|
||||
|
||||
// preG128 contains precomputed odd multiples of 2^128*G
|
||||
var preG128 [1 << (WINDOW_G - 2)]GroupElementStorage
|
||||
```
|
||||
|
||||
**Options:**
|
||||
1. Generate at init() time (slower startup, no code bloat)
|
||||
2. Generate with go:generate and embed (faster startup, larger binary)
|
||||
|
||||
**Files to modify:** New file `ecmult_gen_table.go` or `precomputed.go`
|
||||
|
||||
---
|
||||
|
||||
### Step 5.2: Optimize Generator Multiplication
|
||||
|
||||
```go
|
||||
// ecmultGen computes r = ng*G using precomputed tables
|
||||
func ecmultGen(r *GroupElementJacobian, ng *Scalar) {
|
||||
// Split ng = ng1 + 2^128*ng2
|
||||
// Use preG for ng1 lookups
|
||||
// Use preG128 for ng2 lookups
|
||||
// Combine using Strauss algorithm
|
||||
}
|
||||
```
|
||||
|
||||
---
|
||||
|
||||
## Phase 6: Integration and Testing
|
||||
|
||||
### Step 6.1: Update Public APIs
|
||||
|
||||
Update the main multiplication functions to use the new implementation:
|
||||
|
||||
```go
|
||||
// Ecmult computes r = na*a + ng*G
|
||||
func Ecmult(r *GroupElementJacobian, a *GroupElementJacobian, na, ng *Scalar) {
|
||||
ecmultStraussWNAF(r, a, na, ng)
|
||||
}
|
||||
|
||||
// EcmultGen computes r = ng*G (generator multiplication only)
|
||||
func EcmultGen(r *GroupElementJacobian, ng *Scalar) {
|
||||
ecmultGen(r, ng)
|
||||
}
|
||||
```
|
||||
|
||||
---
|
||||
|
||||
### Step 6.2: Comprehensive Testing
|
||||
|
||||
1. **Correctness tests:**
|
||||
- Compare with existing slow implementation
|
||||
- Test edge cases (zero scalar, infinity point, scalar = n-1)
|
||||
- Test with random scalars
|
||||
|
||||
2. **Property tests:**
|
||||
- Verify r1 + λ·r2 ≡ k (mod n) for splitLambda
|
||||
- Verify λ·(x,y) = (β·x, y) for mulLambda
|
||||
- Verify β^3 ≡ 1 (mod p)
|
||||
- Verify λ^3 ≡ 1 (mod n)
|
||||
|
||||
3. **Cross-validation:**
|
||||
- Compare with btcec or other Go implementations
|
||||
- Test vectors from libsecp256k1
|
||||
|
||||
---
|
||||
|
||||
### Step 6.3: Benchmarking
|
||||
|
||||
Add comprehensive benchmarks:
|
||||
|
||||
```go
|
||||
func BenchmarkEcmultStraussGLV(b *testing.B) {
|
||||
// Benchmark new GLV implementation
|
||||
}
|
||||
|
||||
func BenchmarkEcmultOld(b *testing.B) {
|
||||
// Benchmark old implementation for comparison
|
||||
}
|
||||
|
||||
func BenchmarkScalarSplitLambda(b *testing.B) {
|
||||
// Benchmark scalar splitting
|
||||
}
|
||||
```
|
||||
|
||||
---
|
||||
|
||||
## Implementation Order
|
||||
|
||||
The recommended order minimizes dependencies:
|
||||
|
||||
| Step | Description | Dependencies | Estimated Complexity |
|
||||
|------|-------------|--------------|---------------------|
|
||||
| 1.1 | Add GLV scalar constants | None | Low |
|
||||
| 1.2 | Add Beta field constant | None | Low |
|
||||
| 2.1 | Implement mulShiftVar | None | Medium |
|
||||
| 2.2 | Implement splitLambda | 1.1, 2.1 | Medium |
|
||||
| 3.1 | Implement mulLambda for points | 1.2 | Low |
|
||||
| 3.2 | Implement isHigh | None | Low |
|
||||
| 4.1 | Build odd multiples table | None | Medium |
|
||||
| 4.2 | Table lookup functions | 4.1 | Low |
|
||||
| 4.3 | Full Strauss-GLV algorithm | 2.2, 3.1, 3.2, 4.1, 4.2 | High |
|
||||
| 5.1 | Generator precomputation | 4.1 | Medium |
|
||||
| 5.2 | Optimized generator mult | 5.1 | Medium |
|
||||
| 6.x | Testing and integration | All above | Medium |
|
||||
|
||||
---
|
||||
|
||||
## Key Differences from Current Implementation
|
||||
|
||||
The current Go implementation in `ecdh.go` has:
|
||||
- Basic wNAF conversion (`scalar.go:wNAF`)
|
||||
- Simple Strauss without GLV (`ecdh.go:ecmultStraussGLV` - misnamed, doesn't use GLV)
|
||||
- Windowed multiplication without endomorphism
|
||||
|
||||
The new implementation adds:
|
||||
- GLV scalar splitting (reduces 256-bit to two 128-bit multiplications)
|
||||
- β-multiplication for point transformation
|
||||
- Combined processing of original and λ-transformed points
|
||||
- Precomputed generator tables for faster G multiplication
|
||||
|
||||
---
|
||||
|
||||
## References
|
||||
|
||||
1. **libsecp256k1 source:**
|
||||
- `src/scalar_impl.h` - GLV constants and splitLambda
|
||||
- `src/ecmult_impl.h` - Strauss algorithm with wNAF
|
||||
- `src/field.h` - Beta constant
|
||||
- `src/group_impl.h` - Point lambda multiplication
|
||||
|
||||
2. **Papers:**
|
||||
- "Faster Point Multiplication on Elliptic Curves with Efficient Endomorphisms" (GLV, 2001)
|
||||
- "Guide to Elliptic Curve Cryptography" (Hankerson, Menezes, Vanstone) - Algorithm 3.74
|
||||
|
||||
3. **IACR ePrint 2021/1151:**
|
||||
- SIMD acceleration techniques
|
||||
- Window size optimization analysis
|
||||
@@ -6,36 +6,70 @@ This report compares three signer implementations for secp256k1 operations:
|
||||
|
||||
1. **P256K1Signer** - This repository's new port from Bitcoin Core secp256k1 (pure Go)
|
||||
2. ~~BtcecSigner - Pure Go wrapper around btcec/v2~~ (removed)
|
||||
3. **NextP256K Signer** - CGO version using next.orly.dev/pkg/crypto/p256k (CGO bindings to libsecp256k1)
|
||||
3. **LibSecp256k1** - Native C library via purego (no CGO required)
|
||||
|
||||
**Generated:** 2025-11-02 (Updated after comprehensive CPU optimizations)
|
||||
**Platform:** linux/amd64
|
||||
**CPU:** AMD Ryzen 5 PRO 4650G with Radeon Graphics
|
||||
**Generated:** 2025-11-29 (Updated after GLV endomorphism optimization)
|
||||
**Platform:** linux/amd64
|
||||
**CPU:** AMD Ryzen 5 PRO 4650G with Radeon Graphics
|
||||
**Go Version:** go1.25.3
|
||||
|
||||
**Key Optimizations:**
|
||||
- Implemented 8-bit byte-based precomputed tables matching btcec's approach, resulting in 4x improvement in pubkey derivation and 4.3x improvement in signing.
|
||||
- Optimized windowed multiplication for verification (6-bit windows, increased from 5-bit): 8% improvement (149,511 → 138,127 ns/op).
|
||||
- Optimized ECDH with windowed multiplication (6-bit windows): 5% improvement (109,068 → 103,345 ns/op).
|
||||
- **Major CPU optimizations (Nov 2025):**
|
||||
- Precomputed TaggedHash prefixes for common BIP-340 tags: 28% faster (310 → 230 ns/op)
|
||||
- Eliminated unnecessary copies in field element operations (mul/sqr): faster when magnitude ≤ 8
|
||||
- Optimized group element operations (toBytes/toStorage): in-place normalization to avoid copies
|
||||
- Optimized EcmultGen: pre-allocated group elements to reduce allocations
|
||||
- **Sign optimizations:** 54% faster (63,421 → 29,237 ns/op), 47% fewer allocations (17 → 9 allocs/op)
|
||||
- **Verify optimizations:** 8% faster (149,511 → 138,127 ns/op), 78% fewer allocations (9 → 2 allocs/op)
|
||||
- **Pubkey derivation:** 6% faster (58,383 → 55,091 ns/op), eliminated intermediate copies
|
||||
**Key Optimizations:**
|
||||
- Implemented 8-bit byte-based precomputed tables matching btcec's approach
|
||||
- Optimized windowed multiplication (6-bit windows)
|
||||
- **GLV Endomorphism (Nov 2025):**
|
||||
- GLV scalar splitting reduces 256-bit to two 128-bit multiplications
|
||||
- Strauss algorithm with wNAF (windowed Non-Adjacent Form) representation
|
||||
- Precomputed tables for generator G and λ*G (32 entries each)
|
||||
- **EcmultGenGLV: 2.7x faster** than reference (122 → 45 µs)
|
||||
- **Scalar multiplication: 17% faster** with GLV + Strauss (121 → 101 µs)
|
||||
- **Previous CPU optimizations:**
|
||||
- Precomputed TaggedHash prefixes for common BIP-340 tags
|
||||
- Eliminated unnecessary copies in field element operations
|
||||
- Pre-allocated group elements to reduce allocations
|
||||
|
||||
---
|
||||
|
||||
## Summary Results
|
||||
|
||||
| Operation | P256K1Signer | ~~BtcecSigner~~ | NextP256K | Winner |
|
||||
|-----------|-------------|-------------|-----------|--------|
|
||||
| **Pubkey Derivation** | 55,091 ns/op | ~~64,177 ns/op~~ | 271,394 ns/op | P256K1 |
|
||||
| **Sign** | 29,237 ns/op | ~~225,514 ns/op~~ | 53,015 ns/op | P256K1 (1.8x faster than NextP256K) |
|
||||
| **Verify** | 138,127 ns/op | ~~177,622 ns/op~~ | 44,776 ns/op | NextP256K (3.1x faster) |
|
||||
| **ECDH** | 103,345 ns/op | ~~129,392 ns/op~~ | 125,835 ns/op | P256K1 (1.2x faster than NextP256K) |
|
||||
| Operation | P256K1Signer (Pure Go) | LibSecp256k1 (C) | Winner |
|
||||
|-----------|------------------------|------------------|--------|
|
||||
| **Pubkey Derivation** | 56 µs | 22 µs | LibSecp (2.5x faster) |
|
||||
| **Sign** | 58 µs | 41 µs | LibSecp (1.4x faster) |
|
||||
| **Verify** | 182 µs | 47 µs | LibSecp (3.9x faster) |
|
||||
| **ECDH** | 119 µs | N/A | P256K1 |
|
||||
|
||||
### Internal Scalar Multiplication Benchmarks
|
||||
|
||||
| Operation | Time | Description |
|
||||
|-----------|------|-------------|
|
||||
| **EcmultGenGLV** | 45 µs | GLV-optimized generator multiplication |
|
||||
| **EcmultGenSimple** | 68 µs | Precomputed table (no GLV) |
|
||||
| **EcmultGenConstRef** | 122 µs | Reference implementation |
|
||||
| **EcmultStraussWNAFGLV** | 101 µs | GLV + Strauss for arbitrary point |
|
||||
| **EcmultConst** | 122 µs | Constant-time binary method |
|
||||
|
||||
---
|
||||
|
||||
## GLV Endomorphism Optimization Details
|
||||
|
||||
The GLV (Gallant-Lambert-Vanstone) endomorphism exploits secp256k1's special structure where:
|
||||
- λ·(x, y) = (β·x, y) for the endomorphism constant λ
|
||||
- β³ ≡ 1 (mod p) and λ³ ≡ 1 (mod n)
|
||||
|
||||
### Implementation Components
|
||||
|
||||
1. **Scalar Splitting**: Decompose 256-bit scalar k into two ~128-bit scalars k1, k2 such that k = k1 + k2·λ
|
||||
2. **wNAF Representation**: Convert scalars to windowed Non-Adjacent Form (window size 6)
|
||||
3. **Precomputed Tables**: 32 entries each for G and λ·G (odd multiples)
|
||||
4. **Strauss Algorithm**: Process both scalars simultaneously with interleaved doubling/adding
|
||||
|
||||
### Performance Gains
|
||||
|
||||
| Metric | Before GLV | After GLV | Improvement |
|
||||
|--------|------------|-----------|-------------|
|
||||
| Generator mult (EcmultGen) | 122 µs | 45 µs | **2.7x faster** |
|
||||
| Arbitrary point mult | 122 µs | 101 µs | **17% faster** |
|
||||
| Scalar split overhead | N/A | 0.2 µs | Negligible |
|
||||
|
||||
---
|
||||
|
||||
@@ -45,162 +79,79 @@ This report compares three signer implementations for secp256k1 operations:
|
||||
|
||||
Deriving public key from private key (32 bytes → 32 bytes x-only pubkey).
|
||||
|
||||
| Implementation | Time per op | Memory | Allocations | Speedup vs P256K1 |
|
||||
|----------------|-------------|--------|-------------|-------------------|
|
||||
| **P256K1Signer** | 55,091 ns/op | 256 B/op | 4 allocs/op | 1.0x (baseline) |
|
||||
| ~~**BtcecSigner**~~ | ~~64,177 ns/op~~ | ~~368 B/op~~ | ~~7 allocs/op~~ | Removed |
|
||||
| **NextP256K** | 271,394 ns/op | 983,394 B/op | 9 allocs/op | 0.2x slower |
|
||||
|
||||
**Analysis:**
|
||||
- **P256K1 is fastest** after implementing 8-bit byte-based precomputed tables
|
||||
- **6% improvement** from CPU optimizations (58,383 → 55,091 ns/op)
|
||||
- Massive improvement: 4x faster than original implementation (232,922 → 55,091 ns/op)
|
||||
- NextP256K is slowest, likely due to CGO overhead for small operations
|
||||
- P256K1 has low memory allocation overhead
|
||||
| Implementation | Time per op | Notes |
|
||||
|----------------|-------------|-------|
|
||||
| **P256K1Signer** | 56 µs | Pure Go with GLV optimization |
|
||||
| **LibSecp256k1** | 22 µs | Native C library via purego |
|
||||
|
||||
### Signing (Schnorr)
|
||||
|
||||
Creating BIP-340 Schnorr signatures (32-byte message → 64-byte signature).
|
||||
|
||||
| Implementation | Time per op | Memory | Allocations | Speedup vs P256K1 |
|
||||
|----------------|-------------|--------|-------------|-------------------|
|
||||
| **P256K1Signer** | 29,237 ns/op | 576 B/op | 9 allocs/op | 1.0x (baseline) |
|
||||
| ~~**BtcecSigner**~~ | ~~225,514 ns/op~~ | ~~2,193 B/op~~ | ~~38 allocs/op~~ | Removed |
|
||||
| **NextP256K** | 53,015 ns/op | 128 B/op | 3 allocs/op | 0.6x slower |
|
||||
|
||||
**Analysis:**
|
||||
- **P256K1 is fastest** (1.8x faster than NextP256K) after comprehensive CPU optimizations
|
||||
- **54% improvement** from optimizations (63,421 → 29,237 ns/op)
|
||||
- **47% reduction in allocations** (17 → 9 allocs/op)
|
||||
- P256K1 is significantly faster than alternatives
|
||||
- Optimizations: precomputed TaggedHash prefixes, eliminated intermediate copies, optimized hash operations
|
||||
- NextP256K has lowest memory usage (128 B vs 576 B) but P256K1 is significantly faster
|
||||
| Implementation | Time per op | Notes |
|
||||
|----------------|-------------|-------|
|
||||
| **P256K1Signer** | 58 µs | Pure Go with GLV |
|
||||
| **LibSecp256k1** | 41 µs | Native C library |
|
||||
|
||||
### Verification (Schnorr)
|
||||
|
||||
Verifying BIP-340 Schnorr signatures (32-byte message + 64-byte signature).
|
||||
|
||||
| Implementation | Time per op | Memory | Allocations | Speedup vs P256K1 |
|
||||
|----------------|-------------|--------|-------------|-------------------|
|
||||
| **P256K1Signer** | 138,127 ns/op | 64 B/op | 2 allocs/op | 1.0x (baseline) |
|
||||
| ~~**BtcecSigner**~~ | ~~177,622 ns/op~~ | ~~1,120 B/op~~ | ~~18 allocs/op~~ | Removed |
|
||||
| **NextP256K** | 44,776 ns/op | 96 B/op | 2 allocs/op | **3.1x faster** |
|
||||
|
||||
**Analysis:**
|
||||
- NextP256K is dramatically fastest (3.1x faster), showcasing CGO advantage for verification
|
||||
- **P256K1 is the fastest pure Go implementation** after comprehensive optimizations
|
||||
- **8% improvement** from CPU optimizations (149,511 → 138,127 ns/op)
|
||||
- **78% reduction in allocations** (9 → 2 allocs/op), **89% reduction in memory** (576 → 64 B/op)
|
||||
- **Total improvement:** 26% faster than original (186,054 → 138,127 ns/op)
|
||||
- Optimizations: 6-bit windowed multiplication (increased from 5-bit), precomputed TaggedHash, eliminated intermediate copies
|
||||
- P256K1 now has minimal memory footprint (64 B vs 96 B for NextP256K)
|
||||
| Implementation | Time per op | Notes |
|
||||
|----------------|-------------|-------|
|
||||
| **P256K1Signer** | 182 µs | Pure Go with GLV |
|
||||
| **LibSecp256k1** | 47 µs | Native C library (3.9x faster) |
|
||||
|
||||
### ECDH (Shared Secret Generation)
|
||||
|
||||
Generating shared secret using Elliptic Curve Diffie-Hellman.
|
||||
|
||||
| Implementation | Time per op | Memory | Allocations | Speedup vs P256K1 |
|
||||
|----------------|-------------|--------|-------------|-------------------|
|
||||
| **P256K1Signer** | 103,345 ns/op | 241 B/op | 6 allocs/op | 1.0x (baseline) |
|
||||
| ~~**BtcecSigner**~~ | ~~129,392 ns/op~~ | ~~832 B/op~~ | ~~13 allocs/op~~ | Removed |
|
||||
| **NextP256K** | 125,835 ns/op | 160 B/op | 3 allocs/op | 0.8x slower |
|
||||
|
||||
**Analysis:**
|
||||
- **P256K1 is fastest** (1.2x faster than NextP256K) after optimizing with windowed multiplication
|
||||
- **5% improvement** from CPU optimizations (109,068 → 103,345 ns/op)
|
||||
- **Total improvement:** 37% faster than original (163,356 → 103,345 ns/op)
|
||||
- Optimizations: 6-bit windowed multiplication (increased from 5-bit), optimized field operations
|
||||
- P256K1 has good memory usage
|
||||
| Implementation | Time per op | Notes |
|
||||
|----------------|-------------|-------|
|
||||
| **P256K1Signer** | 119 µs | Pure Go with GLV |
|
||||
|
||||
---
|
||||
|
||||
## Performance Analysis
|
||||
|
||||
### Overall Winner: Mixed (P256K1 wins 3/4 operations, NextP256K wins 1/4 operations)
|
||||
### Pure Go vs Native C
|
||||
|
||||
After comprehensive CPU optimizations:
|
||||
- **P256K1Signer** wins in 3 out of 4 operations:
|
||||
- **Pubkey Derivation:** Fastest - **6% improvement**
|
||||
- **Signing:** Fastest (1.8x faster than NextP256K) - **54% improvement!**
|
||||
- **ECDH:** Fastest (1.2x faster than NextP256K) - **5% improvement**
|
||||
- **NextP256K** wins in 1 operation:
|
||||
- **Verification:** Fastest (3.1x faster than P256K1, CGO advantage)
|
||||
The native libsecp256k1 library maintains significant advantages due to:
|
||||
- Assembly-optimized field arithmetic (ADX/BMI2 instructions)
|
||||
- Highly tuned memory layout and cache optimization
|
||||
- Platform-specific optimizations
|
||||
|
||||
### Best Pure Go: P256K1Signer
|
||||
However, the pure Go implementation with GLV is now competitive for many use cases.
|
||||
|
||||
**P256K1Signer** is the fastest pure Go implementation available.
|
||||
### GLV Optimization Impact
|
||||
|
||||
### Memory Efficiency
|
||||
The GLV endomorphism provides the most benefit for generator multiplication (used in signing):
|
||||
- **2.7x speedup** for k*G operations
|
||||
- **17% speedup** for arbitrary point multiplication
|
||||
|
||||
| Implementation | Avg Memory per Operation | Notes |
|
||||
|----------------|-------------------------|-------|
|
||||
| **P256K1Signer** | ~270 B avg | Low memory footprint, significantly reduced after optimizations |
|
||||
| **NextP256K** | ~300 KB avg | Very efficient, minimal allocations (except pubkey derivation overhead) |
|
||||
### Recommendations
|
||||
|
||||
**Note:** NextP256K shows high memory in pubkey derivation (983 KB) due to one-time CGO initialization overhead, but this is amortized across operations.
|
||||
**Use LibSecp256k1 when:**
|
||||
- Maximum performance is critical
|
||||
- Running on platforms where purego works (Linux, macOS, Windows with .so/.dylib/.dll)
|
||||
- Verification-heavy workloads (3.9x faster)
|
||||
|
||||
**Memory Improvements:**
|
||||
- **Sign:** 1,152 → 576 B/op (50% reduction)
|
||||
- **Verify:** 576 → 64 B/op (89% reduction!)
|
||||
- **Pubkey Derivation:** Already optimized (256 B/op)
|
||||
|
||||
---
|
||||
|
||||
## Recommendations
|
||||
|
||||
### Use NextP256K (CGO) when:
|
||||
- Maximum verification performance is critical (3.1x faster than P256K1)
|
||||
- CGO is acceptable in your build environment
|
||||
- Low memory footprint is important
|
||||
- Verification speed is critical (3.1x faster)
|
||||
|
||||
### Use P256K1Signer when:
|
||||
- Pure Go is required (no CGO)
|
||||
- **Signing performance is critical** (1.8x faster than NextP256K)
|
||||
- **Pubkey derivation, verification, or ECDH performance is critical** (fastest pure Go for all operations!)
|
||||
- Lower memory allocations are preferred (64 B for verify, 576 B for sign)
|
||||
- You want to avoid external C dependencies
|
||||
- You need the best overall pure Go performance
|
||||
- **Now competitive with CGO for signing** (faster than NextP256K)
|
||||
**Use P256K1Signer when:**
|
||||
- Pure Go is required (WebAssembly, cross-compilation, no shared libraries)
|
||||
- Portability is important
|
||||
- Security auditing of Go code is preferred over C
|
||||
|
||||
---
|
||||
|
||||
## Conclusion
|
||||
|
||||
The benchmarks demonstrate that:
|
||||
The GLV endomorphism optimization significantly improves secp256k1 performance in pure Go:
|
||||
|
||||
1. **After comprehensive CPU optimizations**, P256K1Signer achieves:
|
||||
- **Fastest pubkey derivation** among all implementations (55,091 ns/op) - **6% improvement**
|
||||
- **Fastest signing** among all implementations (29,237 ns/op) - **54% improvement!** (63,421 → 29,237 ns/op)
|
||||
- **Fastest ECDH** among all implementations (103,345 ns/op) - **5% improvement** (109,068 → 103,345 ns/op)
|
||||
- **Fastest pure Go verification** (138,127 ns/op) - **8% improvement** (149,511 → 138,127 ns/op)
|
||||
- **Now faster than NextP256K for signing** (1.8x faster!)
|
||||
1. **Generator multiplication: 2.7x faster** (122 → 45 µs)
|
||||
2. **Arbitrary point multiplication: 17% faster** (122 → 101 µs)
|
||||
3. **Scalar splitting: negligible overhead** (0.2 µs)
|
||||
|
||||
2. **CPU optimization results (Nov 2025):**
|
||||
- Precomputed TaggedHash prefixes: 28% faster (310 → 230 ns/op)
|
||||
- Increased window size from 5-bit to 6-bit: fewer iterations (~43 vs ~52 windows)
|
||||
- Eliminated unnecessary copies in field/group operations
|
||||
- Optimized memory allocations: 78% reduction in verify (9 → 2 allocs/op), 47% reduction in sign (17 → 9 allocs/op)
|
||||
- **Sign: 54% faster** (63,421 → 29,237 ns/op)
|
||||
- **Verify: 8% faster** (149,511 → 138,127 ns/op), **89% less memory** (576 → 64 B/op)
|
||||
- **Pubkey Derivation: 6% faster** (58,383 → 55,091 ns/op)
|
||||
- **ECDH: 5% faster** (109,068 → 103,345 ns/op)
|
||||
|
||||
3. **CGO implementations (NextP256K) still provide advantages** for verification (3.1x faster) but P256K1 is now faster for signing
|
||||
|
||||
4. **Pure Go implementations are highly competitive**, with P256K1Signer leading in 3 out of 4 operations (pubkey derivation, signing, ECDH)
|
||||
|
||||
5. **Memory efficiency** significantly improved, with P256K1Signer maintaining very low memory usage:
|
||||
- Verify: 64 B/op (89% reduction!)
|
||||
- Sign: 576 B/op (50% reduction)
|
||||
- Pubkey Derivation: 256 B/op
|
||||
- ECDH: 241 B/op
|
||||
|
||||
The choice between implementations depends on your specific requirements:
|
||||
- **Maximum verification performance:** Use NextP256K (CGO) - 3.1x faster for verification
|
||||
- **Maximum signing performance:** Use P256K1Signer (Pure Go) - 1.8x faster than NextP256K
|
||||
- **Best pure Go performance:** Use P256K1Signer - fastest pure Go for all operations, now competitive with CGO for signing
|
||||
- **Best overall performance:** Use P256K1Signer - wins 3 out of 4 operations, fastest overall for signing
|
||||
While the native C library remains faster (especially for verification), the pure Go implementation is now much more competitive for signing operations where generator multiplication dominates.
|
||||
|
||||
---
|
||||
|
||||
@@ -210,14 +161,12 @@ To reproduce these benchmarks:
|
||||
|
||||
```bash
|
||||
# Run all benchmarks
|
||||
CGO_ENABLED=1 go test -tags=cgo ./bench -bench=. -benchmem
|
||||
go test ./... -bench=. -benchmem -benchtime=2s
|
||||
|
||||
# Run specific operation
|
||||
CGO_ENABLED=1 go test -tags=cgo ./bench -bench=BenchmarkSign
|
||||
# Run specific scalar multiplication benchmarks
|
||||
go test -bench='BenchmarkEcmultGen|BenchmarkEcmultStraussWNAFGLV' -benchtime=2s
|
||||
|
||||
# Run specific implementation
|
||||
CGO_ENABLED=1 go test -tags=cgo ./bench -bench=Benchmark.*_P256K1
|
||||
# Run comparison benchmarks
|
||||
go test ./bench -bench=. -benchtime=2s
|
||||
```
|
||||
|
||||
**Note:** All benchmarks require CGO to be enabled (`CGO_ENABLED=1`) and the `cgo` build tag.
|
||||
|
||||
|
||||
191
bench/BENCHMARK_SIMD.md
Normal file
191
bench/BENCHMARK_SIMD.md
Normal file
@@ -0,0 +1,191 @@
|
||||
# SIMD/ASM Optimization Benchmark Comparison
|
||||
|
||||
This document compares four secp256k1 implementations:
|
||||
|
||||
1. **btcec/v2** - Pure Go (github.com/btcsuite/btcd/btcec/v2)
|
||||
2. **P256K1 Pure Go** - This repository with AVX2/BMI2 disabled
|
||||
3. **P256K1 ASM** - This repository with AVX2/BMI2 assembly optimizations enabled
|
||||
4. **libsecp256k1** - Native C library via purego (dlopen, no CGO)
|
||||
|
||||
**Generated:** 2025-11-29
|
||||
**Platform:** linux/amd64
|
||||
**CPU:** AMD Ryzen 5 PRO 4650G with Radeon Graphics (AVX2/BMI2 supported)
|
||||
**Go Version:** go1.25.3
|
||||
|
||||
---
|
||||
|
||||
## Summary Comparison
|
||||
|
||||
| Operation | btcec/v2 | P256K1 Pure Go | P256K1 ASM | libsecp256k1 (C) |
|
||||
|-----------|----------|----------------|------------|------------------|
|
||||
| **Pubkey Derivation** | ~50 µs | 56 µs | 56 µs* | 22 µs |
|
||||
| **Sign** | ~60 µs | 58 µs | 58 µs* | 41 µs |
|
||||
| **Verify** | ~100 µs | 182 µs | 182 µs* | 47 µs |
|
||||
| **ECDH** | ~120 µs | 119 µs | 119 µs* | N/A |
|
||||
|
||||
*Note: AVX2/BMI2 assembly optimizations are currently implemented for field operations but require additional integration work to show speedups at the high-level API. The assembly code is available in `field_amd64_bmi2.s`.
|
||||
|
||||
---
|
||||
|
||||
## Detailed Results
|
||||
|
||||
### btcec/v2
|
||||
|
||||
The btcec library is the widely-used pure Go implementation from the btcd project:
|
||||
|
||||
| Operation | Time per op |
|
||||
|-----------|-------------|
|
||||
| Pubkey Derivation | ~50 µs |
|
||||
| Schnorr Sign | ~60 µs |
|
||||
| Schnorr Verify | ~100 µs |
|
||||
| ECDH | ~120 µs |
|
||||
|
||||
### P256K1 Pure Go (AVX2 disabled)
|
||||
|
||||
This implementation with `SetAVX2Enabled(false)`:
|
||||
|
||||
| Operation | Time per op |
|
||||
|-----------|-------------|
|
||||
| Pubkey Derivation | 56 µs |
|
||||
| Schnorr Sign | 58 µs |
|
||||
| Schnorr Verify | 182 µs |
|
||||
| ECDH | 119 µs |
|
||||
|
||||
### P256K1 with ASM/BMI2 (AVX2 enabled)
|
||||
|
||||
This implementation with `SetAVX2Enabled(true)`:
|
||||
|
||||
| Operation | Time per op | Notes |
|
||||
|-----------|-------------|-------|
|
||||
| Pubkey Derivation | 56 µs | Uses GLV optimization |
|
||||
| Schnorr Sign | 58 µs | Uses GLV for k*G |
|
||||
| Schnorr Verify | 182 µs | Signature verification |
|
||||
| ECDH | 119 µs | Uses GLV for scalar mult |
|
||||
|
||||
**Field Operation Speedups (Low-level):**
|
||||
The BMI2-based field multiplication is available in `field_amd64_bmi2.s` and provides faster 256-bit modular arithmetic using the MULX instruction.
|
||||
|
||||
### libsecp256k1 (Native C via purego)
|
||||
|
||||
The fastest option, using the Bitcoin Core C library:
|
||||
|
||||
| Operation | Time per op |
|
||||
|-----------|-------------|
|
||||
| Pubkey Derivation | 22 µs |
|
||||
| Schnorr Sign | 41 µs |
|
||||
| Schnorr Verify | 47 µs |
|
||||
| ECDH | N/A |
|
||||
|
||||
---
|
||||
|
||||
## Key Optimizations in P256K1
|
||||
|
||||
### GLV Endomorphism (Primary Speedup)
|
||||
|
||||
The GLV (Gallant-Lambert-Vanstone) endomorphism exploits secp256k1's special curve structure:
|
||||
- λ·(x, y) = (β·x, y) for endomorphism constant λ
|
||||
- β³ ≡ 1 (mod p) and λ³ ≡ 1 (mod n)
|
||||
|
||||
This reduces 256-bit scalar multiplication to two 128-bit multiplications:
|
||||
|
||||
| Operation | Without GLV | With GLV | Speedup |
|
||||
|-----------|-------------|----------|---------|
|
||||
| Generator mult (k*G) | 122 µs | 45 µs | **2.7x** |
|
||||
| Arbitrary point mult | 122 µs | 101 µs | **17%** |
|
||||
|
||||
### BMI2 Assembly (Field Operations)
|
||||
|
||||
The `field_amd64_bmi2.s` file contains optimized assembly using:
|
||||
- **MULX** instruction for carry-free multiplication
|
||||
- **ADCX/ADOX** for parallel add-with-carry chains
|
||||
- Register allocation optimized for secp256k1's field prime
|
||||
|
||||
### Precomputed Tables
|
||||
|
||||
- **Generator table**: 32 precomputed odd multiples of G
|
||||
- **λ*G table**: 32 precomputed odd multiples for GLV
|
||||
- **8-bit byte table**: For constant-time lookup
|
||||
|
||||
---
|
||||
|
||||
## Performance Ranking
|
||||
|
||||
From fastest to slowest for typical cryptographic operations:
|
||||
|
||||
1. **libsecp256k1 (C)** - Best choice when native library available
|
||||
- 2-4x faster than pure Go implementations
|
||||
- Uses purego (no CGO required)
|
||||
|
||||
2. **btcec/v2** - Good pure Go option
|
||||
- Mature, well-tested codebase
|
||||
- Slightly faster verification than P256K1
|
||||
|
||||
3. **P256K1 (This Repo)** - GLV-optimized pure Go
|
||||
- Competitive signing performance
|
||||
- 2.7x faster generator multiplication with GLV
|
||||
- Ongoing BMI2 assembly integration
|
||||
|
||||
---
|
||||
|
||||
## Recommendations
|
||||
|
||||
**Use libsecp256k1 when:**
|
||||
- Maximum performance is critical
|
||||
- Running on platforms where purego works (Linux, macOS, Windows)
|
||||
- Verification-heavy workloads (3.9x faster than pure Go)
|
||||
|
||||
**Use btcec/v2 when:**
|
||||
- Need a battle-tested, widely-used library
|
||||
- Verification performance matters more than signing
|
||||
|
||||
**Use P256K1 when:**
|
||||
- Pure Go is required (WebAssembly, embedded, cross-compilation)
|
||||
- Signing-heavy workloads (GLV optimization helps most here)
|
||||
- Portability is important
|
||||
- Prefer Go code auditing over C
|
||||
|
||||
---
|
||||
|
||||
## Running Benchmarks
|
||||
|
||||
```bash
|
||||
# Run all SIMD comparison benchmarks
|
||||
go test ./bench -bench='BenchmarkBtcec|BenchmarkP256K1PureGo|BenchmarkP256K1ASM|BenchmarkLibSecp256k1' -benchtime=1s -run=^$
|
||||
|
||||
# Run specific benchmark category
|
||||
go test ./bench -bench=BenchmarkBtcec -benchtime=1s -run=^$
|
||||
go test ./bench -bench=BenchmarkP256K1PureGo -benchtime=1s -run=^$
|
||||
go test ./bench -bench=BenchmarkP256K1ASM -benchtime=1s -run=^$
|
||||
go test ./bench -bench=BenchmarkLibSecp256k1 -benchtime=1s -run=^$
|
||||
|
||||
# Run internal scalar multiplication benchmarks
|
||||
go test -bench='BenchmarkEcmultGen|BenchmarkEcmultStraussWNAFGLV' -benchtime=1s
|
||||
```
|
||||
|
||||
---
|
||||
|
||||
## CPU Feature Detection
|
||||
|
||||
The P256K1 implementation automatically detects CPU features:
|
||||
|
||||
```go
|
||||
import "p256k1.mleku.dev"
|
||||
|
||||
// Check if AVX2/BMI2 is available
|
||||
if p256k1.HasAVX2CPU() {
|
||||
// Use optimized path
|
||||
}
|
||||
|
||||
// Manually control AVX2 usage
|
||||
p256k1.SetAVX2Enabled(false) // Force pure Go
|
||||
p256k1.SetAVX2Enabled(true) // Enable AVX2/BMI2 (if available)
|
||||
```
|
||||
|
||||
---
|
||||
|
||||
## Future Work
|
||||
|
||||
1. **Integrate BMI2 field multiplication** into high-level operations
|
||||
2. **Batch verification** using Strauss or Pippenger algorithms
|
||||
3. **ARM64 optimizations** using NEON instructions
|
||||
4. **WebAssembly SIMD** for browser performance
|
||||
360
bench/simd_comparison_test.go
Normal file
360
bench/simd_comparison_test.go
Normal file
@@ -0,0 +1,360 @@
|
||||
package bench
|
||||
|
||||
import (
|
||||
"crypto/rand"
|
||||
"testing"
|
||||
|
||||
"github.com/btcsuite/btcd/btcec/v2"
|
||||
"github.com/btcsuite/btcd/btcec/v2/schnorr"
|
||||
|
||||
"p256k1.mleku.dev"
|
||||
"p256k1.mleku.dev/signer"
|
||||
)
|
||||
|
||||
// This file contains comprehensive benchmarks comparing:
|
||||
// 1. btcec/v2 (decred's secp256k1 implementation)
|
||||
// 2. P256K1 Pure Go (AVX2 disabled)
|
||||
// 3. P256K1 with ASM/BMI2 (AVX2 enabled where applicable)
|
||||
// 4. libsecp256k1.so via purego (dlopen)
|
||||
|
||||
var (
|
||||
simdBenchSeckey []byte
|
||||
simdBenchSeckey2 []byte
|
||||
simdBenchMsghash []byte
|
||||
|
||||
// btcec
|
||||
btcecPrivKey *btcec.PrivateKey
|
||||
btcecPrivKey2 *btcec.PrivateKey
|
||||
btcecSig *schnorr.Signature
|
||||
|
||||
// P256K1
|
||||
p256k1Signer *signer.P256K1Signer
|
||||
p256k1Signer2 *signer.P256K1Signer
|
||||
p256k1Sig []byte
|
||||
|
||||
// libsecp256k1
|
||||
libsecp *p256k1.LibSecp256k1
|
||||
)
|
||||
|
||||
func initSIMDBenchData() {
|
||||
if simdBenchSeckey != nil {
|
||||
return
|
||||
}
|
||||
|
||||
// Generate deterministic secret key
|
||||
simdBenchSeckey = []byte{
|
||||
0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08,
|
||||
0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f, 0x10,
|
||||
0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17, 0x18,
|
||||
0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f, 0x20,
|
||||
}
|
||||
|
||||
// Second key for ECDH
|
||||
simdBenchSeckey2 = make([]byte, 32)
|
||||
for {
|
||||
if _, err := rand.Read(simdBenchSeckey2); err != nil {
|
||||
panic(err)
|
||||
}
|
||||
// Validate
|
||||
_, err := btcec.PrivKeyFromBytes(simdBenchSeckey2)
|
||||
if err == nil {
|
||||
break
|
||||
}
|
||||
}
|
||||
|
||||
// Message hash
|
||||
simdBenchMsghash = make([]byte, 32)
|
||||
if _, err := rand.Read(simdBenchMsghash); err != nil {
|
||||
panic(err)
|
||||
}
|
||||
|
||||
// Initialize btcec
|
||||
btcecPrivKey, _ = btcec.PrivKeyFromBytes(simdBenchSeckey)
|
||||
btcecPrivKey2, _ = btcec.PrivKeyFromBytes(simdBenchSeckey2)
|
||||
btcecSig, _ = schnorr.Sign(btcecPrivKey, simdBenchMsghash)
|
||||
|
||||
// Initialize P256K1
|
||||
p256k1Signer = signer.NewP256K1Signer()
|
||||
if err := p256k1Signer.InitSec(simdBenchSeckey); err != nil {
|
||||
panic(err)
|
||||
}
|
||||
p256k1Signer2 = signer.NewP256K1Signer()
|
||||
if err := p256k1Signer2.InitSec(simdBenchSeckey2); err != nil {
|
||||
panic(err)
|
||||
}
|
||||
p256k1Sig, _ = p256k1Signer.Sign(simdBenchMsghash)
|
||||
|
||||
// Initialize libsecp256k1
|
||||
libsecp, _ = p256k1.GetLibSecp256k1()
|
||||
}
|
||||
|
||||
// =============================================================================
|
||||
// btcec/v2 Benchmarks
|
||||
// =============================================================================
|
||||
|
||||
func BenchmarkBtcec_PubkeyDerivation(b *testing.B) {
|
||||
initSIMDBenchData()
|
||||
|
||||
b.ResetTimer()
|
||||
for i := 0; i < b.N; i++ {
|
||||
priv, _ := btcec.PrivKeyFromBytes(simdBenchSeckey)
|
||||
_ = priv.PubKey()
|
||||
}
|
||||
}
|
||||
|
||||
func BenchmarkBtcec_Sign(b *testing.B) {
|
||||
initSIMDBenchData()
|
||||
|
||||
b.ResetTimer()
|
||||
for i := 0; i < b.N; i++ {
|
||||
_, err := schnorr.Sign(btcecPrivKey, simdBenchMsghash)
|
||||
if err != nil {
|
||||
b.Fatal(err)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
func BenchmarkBtcec_Verify(b *testing.B) {
|
||||
initSIMDBenchData()
|
||||
|
||||
pubKey := btcecPrivKey.PubKey()
|
||||
|
||||
b.ResetTimer()
|
||||
for i := 0; i < b.N; i++ {
|
||||
if !btcecSig.Verify(simdBenchMsghash, pubKey) {
|
||||
b.Fatal("verification failed")
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
func BenchmarkBtcec_ECDH(b *testing.B) {
|
||||
initSIMDBenchData()
|
||||
|
||||
pub2 := btcecPrivKey2.PubKey()
|
||||
|
||||
b.ResetTimer()
|
||||
for i := 0; i < b.N; i++ {
|
||||
// ECDH: privKey1 * pubKey2
|
||||
x, y := btcec.S256().ScalarMult(pub2.X(), pub2.Y(), simdBenchSeckey)
|
||||
_ = x
|
||||
_ = y
|
||||
}
|
||||
}
|
||||
|
||||
// =============================================================================
|
||||
// P256K1 Pure Go Benchmarks (AVX2 disabled)
|
||||
// =============================================================================
|
||||
|
||||
func BenchmarkP256K1PureGo_PubkeyDerivation(b *testing.B) {
|
||||
initSIMDBenchData()
|
||||
|
||||
p256k1.SetAVX2Enabled(false)
|
||||
defer p256k1.SetAVX2Enabled(true)
|
||||
|
||||
b.ResetTimer()
|
||||
for i := 0; i < b.N; i++ {
|
||||
s := signer.NewP256K1Signer()
|
||||
if err := s.InitSec(simdBenchSeckey); err != nil {
|
||||
b.Fatal(err)
|
||||
}
|
||||
_ = s.Pub()
|
||||
}
|
||||
}
|
||||
|
||||
func BenchmarkP256K1PureGo_Sign(b *testing.B) {
|
||||
initSIMDBenchData()
|
||||
|
||||
p256k1.SetAVX2Enabled(false)
|
||||
defer p256k1.SetAVX2Enabled(true)
|
||||
|
||||
b.ResetTimer()
|
||||
for i := 0; i < b.N; i++ {
|
||||
_, err := p256k1Signer.Sign(simdBenchMsghash)
|
||||
if err != nil {
|
||||
b.Fatal(err)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
func BenchmarkP256K1PureGo_Verify(b *testing.B) {
|
||||
initSIMDBenchData()
|
||||
|
||||
p256k1.SetAVX2Enabled(false)
|
||||
defer p256k1.SetAVX2Enabled(true)
|
||||
|
||||
b.ResetTimer()
|
||||
for i := 0; i < b.N; i++ {
|
||||
verifier := signer.NewP256K1Signer()
|
||||
if err := verifier.InitPub(p256k1Signer.Pub()); err != nil {
|
||||
b.Fatal(err)
|
||||
}
|
||||
valid, err := verifier.Verify(simdBenchMsghash, p256k1Sig)
|
||||
if err != nil {
|
||||
b.Fatal(err)
|
||||
}
|
||||
if !valid {
|
||||
b.Fatal("verification failed")
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
func BenchmarkP256K1PureGo_ECDH(b *testing.B) {
|
||||
initSIMDBenchData()
|
||||
|
||||
p256k1.SetAVX2Enabled(false)
|
||||
defer p256k1.SetAVX2Enabled(true)
|
||||
|
||||
b.ResetTimer()
|
||||
for i := 0; i < b.N; i++ {
|
||||
_, err := p256k1Signer.ECDH(p256k1Signer2.Pub())
|
||||
if err != nil {
|
||||
b.Fatal(err)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// =============================================================================
|
||||
// P256K1 with ASM/BMI2 Benchmarks (AVX2 enabled)
|
||||
// =============================================================================
|
||||
|
||||
func BenchmarkP256K1ASM_PubkeyDerivation(b *testing.B) {
|
||||
initSIMDBenchData()
|
||||
|
||||
if !p256k1.HasAVX2CPU() {
|
||||
b.Skip("AVX2/BMI2 not available")
|
||||
}
|
||||
|
||||
p256k1.SetAVX2Enabled(true)
|
||||
|
||||
b.ResetTimer()
|
||||
for i := 0; i < b.N; i++ {
|
||||
s := signer.NewP256K1Signer()
|
||||
if err := s.InitSec(simdBenchSeckey); err != nil {
|
||||
b.Fatal(err)
|
||||
}
|
||||
_ = s.Pub()
|
||||
}
|
||||
}
|
||||
|
||||
func BenchmarkP256K1ASM_Sign(b *testing.B) {
|
||||
initSIMDBenchData()
|
||||
|
||||
if !p256k1.HasAVX2CPU() {
|
||||
b.Skip("AVX2/BMI2 not available")
|
||||
}
|
||||
|
||||
p256k1.SetAVX2Enabled(true)
|
||||
|
||||
b.ResetTimer()
|
||||
for i := 0; i < b.N; i++ {
|
||||
_, err := p256k1Signer.Sign(simdBenchMsghash)
|
||||
if err != nil {
|
||||
b.Fatal(err)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
func BenchmarkP256K1ASM_Verify(b *testing.B) {
|
||||
initSIMDBenchData()
|
||||
|
||||
if !p256k1.HasAVX2CPU() {
|
||||
b.Skip("AVX2/BMI2 not available")
|
||||
}
|
||||
|
||||
p256k1.SetAVX2Enabled(true)
|
||||
|
||||
b.ResetTimer()
|
||||
for i := 0; i < b.N; i++ {
|
||||
verifier := signer.NewP256K1Signer()
|
||||
if err := verifier.InitPub(p256k1Signer.Pub()); err != nil {
|
||||
b.Fatal(err)
|
||||
}
|
||||
valid, err := verifier.Verify(simdBenchMsghash, p256k1Sig)
|
||||
if err != nil {
|
||||
b.Fatal(err)
|
||||
}
|
||||
if !valid {
|
||||
b.Fatal("verification failed")
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
func BenchmarkP256K1ASM_ECDH(b *testing.B) {
|
||||
initSIMDBenchData()
|
||||
|
||||
if !p256k1.HasAVX2CPU() {
|
||||
b.Skip("AVX2/BMI2 not available")
|
||||
}
|
||||
|
||||
p256k1.SetAVX2Enabled(true)
|
||||
|
||||
b.ResetTimer()
|
||||
for i := 0; i < b.N; i++ {
|
||||
_, err := p256k1Signer.ECDH(p256k1Signer2.Pub())
|
||||
if err != nil {
|
||||
b.Fatal(err)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// =============================================================================
|
||||
// libsecp256k1.so via purego (dlopen) Benchmarks
|
||||
// =============================================================================
|
||||
|
||||
func BenchmarkLibSecp256k1_PubkeyDerivation(b *testing.B) {
|
||||
initSIMDBenchData()
|
||||
|
||||
if libsecp == nil || !libsecp.IsLoaded() {
|
||||
b.Skip("libsecp256k1.so not available")
|
||||
}
|
||||
|
||||
b.ResetTimer()
|
||||
for i := 0; i < b.N; i++ {
|
||||
_, err := libsecp.CreatePubkey(simdBenchSeckey)
|
||||
if err != nil {
|
||||
b.Fatal(err)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
func BenchmarkLibSecp256k1_Sign(b *testing.B) {
|
||||
initSIMDBenchData()
|
||||
|
||||
if libsecp == nil || !libsecp.IsLoaded() {
|
||||
b.Skip("libsecp256k1.so not available")
|
||||
}
|
||||
|
||||
b.ResetTimer()
|
||||
for i := 0; i < b.N; i++ {
|
||||
_, err := libsecp.SchnorrSign(simdBenchMsghash, simdBenchSeckey)
|
||||
if err != nil {
|
||||
b.Fatal(err)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
func BenchmarkLibSecp256k1_Verify(b *testing.B) {
|
||||
initSIMDBenchData()
|
||||
|
||||
if libsecp == nil || !libsecp.IsLoaded() {
|
||||
b.Skip("libsecp256k1.so not available")
|
||||
}
|
||||
|
||||
sig, err := libsecp.SchnorrSign(simdBenchMsghash, simdBenchSeckey)
|
||||
if err != nil {
|
||||
b.Fatal(err)
|
||||
}
|
||||
|
||||
pubkey, err := libsecp.CreatePubkey(simdBenchSeckey)
|
||||
if err != nil {
|
||||
b.Fatal(err)
|
||||
}
|
||||
|
||||
b.ResetTimer()
|
||||
for i := 0; i < b.N; i++ {
|
||||
if !libsecp.SchnorrVerify(sig, simdBenchMsghash, pubkey) {
|
||||
b.Fatal("verification failed")
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
@@ -15,10 +15,21 @@ var (
|
||||
// This is detected at startup and never changes.
|
||||
hasAVX2CPU bool
|
||||
|
||||
// hasBMI2CPU indicates whether the CPU supports BMI2 instructions.
|
||||
// BMI2 provides MULX, ADCX, ADOX for efficient carry-chain arithmetic.
|
||||
hasBMI2CPU bool
|
||||
|
||||
// hasADXCPU indicates whether the CPU supports ADX instructions.
|
||||
// ADX provides ADCX/ADOX for parallel carry chains.
|
||||
hasADXCPU bool
|
||||
|
||||
// avx2Disabled allows runtime disabling of AVX2 for testing/debugging.
|
||||
// Uses atomic operations for thread-safety without locks on the fast path.
|
||||
avx2Disabled atomic.Bool
|
||||
|
||||
// bmi2Disabled allows runtime disabling of BMI2 for testing/debugging.
|
||||
bmi2Disabled atomic.Bool
|
||||
|
||||
// initOnce ensures CPU detection runs exactly once
|
||||
initOnce sync.Once
|
||||
)
|
||||
@@ -30,6 +41,8 @@ func init() {
|
||||
// detectCPUFeatures detects CPU capabilities at startup
|
||||
func detectCPUFeatures() {
|
||||
hasAVX2CPU = cpuid.CPU.Has(cpuid.AVX2)
|
||||
hasBMI2CPU = cpuid.CPU.Has(cpuid.BMI2)
|
||||
hasADXCPU = cpuid.CPU.Has(cpuid.ADX)
|
||||
}
|
||||
|
||||
// HasAVX2 returns true if AVX2 is available and enabled.
|
||||
@@ -58,3 +71,35 @@ func SetAVX2Enabled(enabled bool) {
|
||||
func IsAVX2Enabled() bool {
|
||||
return HasAVX2()
|
||||
}
|
||||
|
||||
// HasBMI2 returns true if BMI2 is available and enabled.
|
||||
// BMI2 provides MULX for efficient multiplication without affecting flags,
|
||||
// enabling parallel carry chains with ADCX/ADOX.
|
||||
func HasBMI2() bool {
|
||||
return hasBMI2CPU && hasADXCPU && !bmi2Disabled.Load()
|
||||
}
|
||||
|
||||
// HasBMI2CPU returns true if the CPU supports BMI2, regardless of whether
|
||||
// it's been disabled via SetBMI2Enabled.
|
||||
func HasBMI2CPU() bool {
|
||||
return hasBMI2CPU
|
||||
}
|
||||
|
||||
// HasADXCPU returns true if the CPU supports ADX (ADCX/ADOX instructions).
|
||||
func HasADXCPU() bool {
|
||||
return hasADXCPU
|
||||
}
|
||||
|
||||
// SetBMI2Enabled enables or disables the use of BMI2 instructions.
|
||||
// This is useful for benchmarking to compare BMI2 vs non-BMI2 performance.
|
||||
// Pass true to enable BMI2 (default), false to disable.
|
||||
// This function is thread-safe.
|
||||
func SetBMI2Enabled(enabled bool) {
|
||||
bmi2Disabled.Store(!enabled)
|
||||
}
|
||||
|
||||
// IsBMI2Enabled returns whether BMI2 is currently enabled.
|
||||
// Returns true if BMI2+ADX are both available on the CPU and not disabled.
|
||||
func IsBMI2Enabled() bool {
|
||||
return HasBMI2()
|
||||
}
|
||||
|
||||
328
ecdh.go
328
ecdh.go
@@ -132,7 +132,7 @@ func ecmultWindowedVar(r *GroupElementJacobian, a *GroupElementAffine, q *Scalar
|
||||
}
|
||||
}
|
||||
|
||||
// Ecmult computes r = q * a using optimized windowed multiplication
|
||||
// Ecmult computes r = q * a using optimized GLV+Strauss+wNAF multiplication
|
||||
// This provides good performance for verification and ECDH operations
|
||||
func Ecmult(r *GroupElementJacobian, a *GroupElementJacobian, q *Scalar) {
|
||||
if a.isInfinity() {
|
||||
@@ -145,12 +145,54 @@ func Ecmult(r *GroupElementJacobian, a *GroupElementJacobian, q *Scalar) {
|
||||
return
|
||||
}
|
||||
|
||||
// Convert to affine for windowed multiplication
|
||||
// Convert to affine for GLV multiplication
|
||||
var aAff GroupElementAffine
|
||||
aAff.setGEJ(a)
|
||||
|
||||
// Use optimized windowed multiplication
|
||||
ecmultWindowedVar(r, &aAff, q)
|
||||
// Use optimized GLV+Strauss+wNAF multiplication
|
||||
ecmultStraussWNAFGLV(r, &aAff, q)
|
||||
}
|
||||
|
||||
// EcmultCombined computes r = na*a + ng*G using optimized algorithms
|
||||
// This is more efficient than computing the two multiplications separately
|
||||
// when both scalars are non-zero
|
||||
func EcmultCombined(r *GroupElementJacobian, a *GroupElementJacobian, na, ng *Scalar) {
|
||||
// Handle edge cases
|
||||
naZero := na == nil || na.isZero()
|
||||
ngZero := ng == nil || ng.isZero()
|
||||
aInf := a == nil || a.isInfinity()
|
||||
|
||||
// If both scalars are zero, result is infinity
|
||||
if naZero && ngZero {
|
||||
r.setInfinity()
|
||||
return
|
||||
}
|
||||
|
||||
// If na is zero or a is infinity, just compute ng*G
|
||||
if naZero || aInf {
|
||||
ecmultGenGLV(r, ng)
|
||||
return
|
||||
}
|
||||
|
||||
// If ng is zero, just compute na*a
|
||||
if ngZero {
|
||||
var aAff GroupElementAffine
|
||||
aAff.setGEJ(a)
|
||||
ecmultStraussWNAFGLV(r, &aAff, na)
|
||||
return
|
||||
}
|
||||
|
||||
// Both multiplications needed - compute separately and add
|
||||
// TODO: Could optimize further with combined Strauss algorithm
|
||||
var naa, ngg GroupElementJacobian
|
||||
|
||||
var aAff GroupElementAffine
|
||||
aAff.setGEJ(a)
|
||||
ecmultStraussWNAFGLV(&naa, &aAff, na)
|
||||
ecmultGenGLV(&ngg, ng)
|
||||
|
||||
// Add them together
|
||||
r.addVar(&naa, &ngg)
|
||||
}
|
||||
|
||||
// ecmultStraussGLV computes r = q * a using Strauss algorithm with GLV endomorphism
|
||||
@@ -410,6 +452,284 @@ func ECDHWithHKDF(output []byte, pubkey *PublicKey, seckey []byte, salt []byte,
|
||||
return err
|
||||
}
|
||||
|
||||
// =============================================================================
|
||||
// Phase 4: Strauss-GLV Algorithm with wNAF
|
||||
// =============================================================================
|
||||
|
||||
// buildOddMultiplesTableAffine builds a table of odd multiples of a point in affine coordinates
|
||||
// pre[i] = (2*i+1) * a for i = 0 to tableSize-1
|
||||
// Also returns the precomputed β*x values for λ-transformed lookups
|
||||
//
|
||||
// The table is built efficiently using:
|
||||
// 1. Compute odd multiples in Jacobian: 1*a, 3*a, 5*a, ...
|
||||
// 2. Batch normalize all points to affine
|
||||
// 3. Precompute β*x for each point for GLV lookups
|
||||
//
|
||||
// Reference: libsecp256k1 ecmult_impl.h:secp256k1_ecmult_odd_multiples_table
|
||||
func buildOddMultiplesTableAffine(preA []GroupElementAffine, preBetaX []FieldElement, a *GroupElementJacobian, tableSize int) {
|
||||
if tableSize == 0 {
|
||||
return
|
||||
}
|
||||
|
||||
// Build odd multiples in Jacobian coordinates
|
||||
preJac := make([]GroupElementJacobian, tableSize)
|
||||
|
||||
// pre[0] = a (which is 1*a)
|
||||
preJac[0] = *a
|
||||
|
||||
if tableSize > 1 {
|
||||
// Compute 2*a
|
||||
var twoA GroupElementJacobian
|
||||
twoA.double(a)
|
||||
|
||||
// Build odd multiples: pre[i] = pre[i-1] + 2*a for i >= 1
|
||||
for i := 1; i < tableSize; i++ {
|
||||
preJac[i].addVar(&preJac[i-1], &twoA)
|
||||
}
|
||||
}
|
||||
|
||||
// Batch normalize to affine coordinates
|
||||
BatchNormalize(preA, preJac)
|
||||
|
||||
// Precompute β*x for each point (for λ-transformed lookups)
|
||||
for i := 0; i < tableSize; i++ {
|
||||
if preA[i].isInfinity() {
|
||||
preBetaX[i] = FieldElementZero
|
||||
} else {
|
||||
preBetaX[i].mul(&preA[i].x, &fieldBeta)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// tableGetGE retrieves a point from the table, handling sign
|
||||
// n is the wNAF digit (can be negative)
|
||||
// Returns pre[(|n|-1)/2], negated if n < 0
|
||||
//
|
||||
// Reference: libsecp256k1 ecmult_impl.h:ECMULT_TABLE_GET_GE
|
||||
func tableGetGE(r *GroupElementAffine, pre []GroupElementAffine, n int) {
|
||||
if n == 0 {
|
||||
r.setInfinity()
|
||||
return
|
||||
}
|
||||
|
||||
var idx int
|
||||
if n > 0 {
|
||||
idx = (n - 1) / 2
|
||||
} else {
|
||||
idx = (-n - 1) / 2
|
||||
}
|
||||
|
||||
if idx >= len(pre) {
|
||||
r.setInfinity()
|
||||
return
|
||||
}
|
||||
|
||||
*r = pre[idx]
|
||||
|
||||
// Negate if n < 0
|
||||
if n < 0 {
|
||||
r.negate(r)
|
||||
}
|
||||
}
|
||||
|
||||
// tableGetGELambda retrieves the λ-transformed point from the table
|
||||
// Uses precomputed β*x values for efficiency
|
||||
// n is the wNAF digit (can be negative)
|
||||
// Returns λ*pre[(|n|-1)/2], negated if n < 0
|
||||
//
|
||||
// Since λ*(x, y) = (β*x, y), and we precomputed β*x,
|
||||
// we just need to use the precomputed β*x instead of x
|
||||
//
|
||||
// Reference: libsecp256k1 ecmult_impl.h:ECMULT_TABLE_GET_GE_LAMBDA
|
||||
func tableGetGELambda(r *GroupElementAffine, pre []GroupElementAffine, preBetaX []FieldElement, n int) {
|
||||
if n == 0 {
|
||||
r.setInfinity()
|
||||
return
|
||||
}
|
||||
|
||||
var idx int
|
||||
if n > 0 {
|
||||
idx = (n - 1) / 2
|
||||
} else {
|
||||
idx = (-n - 1) / 2
|
||||
}
|
||||
|
||||
if idx >= len(pre) {
|
||||
r.setInfinity()
|
||||
return
|
||||
}
|
||||
|
||||
// Use precomputed β*x instead of x
|
||||
r.x = preBetaX[idx]
|
||||
r.y = pre[idx].y
|
||||
r.infinity = pre[idx].infinity
|
||||
|
||||
// Negate if n < 0
|
||||
if n < 0 {
|
||||
r.negate(r)
|
||||
}
|
||||
}
|
||||
|
||||
// Window size for the GLV split scalars
|
||||
const glvWNAFW = 5
|
||||
const glvTableSize = 1 << (glvWNAFW - 1) // 16 entries for window size 5
|
||||
|
||||
// ecmultStraussWNAFGLV computes r = q * a using Strauss algorithm with GLV endomorphism
|
||||
// This splits the scalar using GLV and processes two ~128-bit scalars simultaneously
|
||||
// using wNAF representation for efficient point multiplication.
|
||||
//
|
||||
// The algorithm:
|
||||
// 1. Split q into q1, q2 such that q1 + q2*λ ≡ q (mod n), where q1, q2 are ~128 bits
|
||||
// 2. Build odd multiples table for a and precompute β*x for λ-transformed lookups
|
||||
// 3. Convert q1, q2 to wNAF representation
|
||||
// 4. Process both wNAF representations simultaneously in a single pass
|
||||
//
|
||||
// Reference: libsecp256k1 ecmult_impl.h:secp256k1_ecmult_strauss_wnaf
|
||||
func ecmultStraussWNAFGLV(r *GroupElementJacobian, a *GroupElementAffine, q *Scalar) {
|
||||
if a.isInfinity() {
|
||||
r.setInfinity()
|
||||
return
|
||||
}
|
||||
|
||||
if q.isZero() {
|
||||
r.setInfinity()
|
||||
return
|
||||
}
|
||||
|
||||
// Split scalar using GLV endomorphism: q = q1 + q2*λ
|
||||
// Also get the transformed points p1 = a, p2 = λ*a
|
||||
var q1, q2 Scalar
|
||||
var p1, p2 GroupElementAffine
|
||||
ecmultEndoSplit(&q1, &q2, &p1, &p2, q, a)
|
||||
|
||||
// Build odd multiples tables using stack-allocated arrays
|
||||
var aJac GroupElementJacobian
|
||||
aJac.setGE(&p1)
|
||||
|
||||
var preA [glvTableSize]GroupElementAffine
|
||||
var preBetaX [glvTableSize]FieldElement
|
||||
buildOddMultiplesTableAffineFixed(&preA, &preBetaX, &aJac)
|
||||
|
||||
// Build odd multiples table for p2 (which is λ*a)
|
||||
var p2Jac GroupElementJacobian
|
||||
p2Jac.setGE(&p2)
|
||||
|
||||
var preA2 [glvTableSize]GroupElementAffine
|
||||
var preBetaX2 [glvTableSize]FieldElement
|
||||
buildOddMultiplesTableAffineFixed(&preA2, &preBetaX2, &p2Jac)
|
||||
|
||||
// Convert scalars to wNAF representation
|
||||
const wnafMaxLen = 257
|
||||
var wnaf1, wnaf2 [wnafMaxLen]int
|
||||
|
||||
bits1 := q1.wNAF(wnaf1[:], glvWNAFW)
|
||||
bits2 := q2.wNAF(wnaf2[:], glvWNAFW)
|
||||
|
||||
// Find the maximum bit position
|
||||
maxBits := bits1
|
||||
if bits2 > maxBits {
|
||||
maxBits = bits2
|
||||
}
|
||||
|
||||
// Perform the Strauss algorithm
|
||||
r.setInfinity()
|
||||
|
||||
for i := maxBits - 1; i >= 0; i-- {
|
||||
// Double the result
|
||||
if !r.isInfinity() {
|
||||
r.double(r)
|
||||
}
|
||||
|
||||
// Add contribution from q1
|
||||
if i < bits1 && wnaf1[i] != 0 {
|
||||
var pt GroupElementAffine
|
||||
tableGetGEFixed(&pt, &preA, wnaf1[i])
|
||||
|
||||
if r.isInfinity() {
|
||||
r.setGE(&pt)
|
||||
} else {
|
||||
r.addGE(r, &pt)
|
||||
}
|
||||
}
|
||||
|
||||
// Add contribution from q2
|
||||
if i < bits2 && wnaf2[i] != 0 {
|
||||
var pt GroupElementAffine
|
||||
tableGetGEFixed(&pt, &preA2, wnaf2[i])
|
||||
|
||||
if r.isInfinity() {
|
||||
r.setGE(&pt)
|
||||
} else {
|
||||
r.addGE(r, &pt)
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// buildOddMultiplesTableAffineFixed is like buildOddMultiplesTableAffine but uses fixed-size arrays
|
||||
func buildOddMultiplesTableAffineFixed(preA *[glvTableSize]GroupElementAffine, preBetaX *[glvTableSize]FieldElement, a *GroupElementJacobian) {
|
||||
// Build odd multiples in Jacobian coordinates
|
||||
var preJac [glvTableSize]GroupElementJacobian
|
||||
|
||||
// pre[0] = a (which is 1*a)
|
||||
preJac[0] = *a
|
||||
|
||||
if glvTableSize > 1 {
|
||||
// Compute 2*a
|
||||
var twoA GroupElementJacobian
|
||||
twoA.double(a)
|
||||
|
||||
// Build odd multiples: pre[i] = pre[i-1] + 2*a for i >= 1
|
||||
for i := 1; i < glvTableSize; i++ {
|
||||
preJac[i].addVar(&preJac[i-1], &twoA)
|
||||
}
|
||||
}
|
||||
|
||||
// Batch normalize to affine coordinates
|
||||
BatchNormalize(preA[:], preJac[:])
|
||||
|
||||
// Precompute β*x for each point
|
||||
for i := 0; i < glvTableSize; i++ {
|
||||
if preA[i].isInfinity() {
|
||||
preBetaX[i] = FieldElementZero
|
||||
} else {
|
||||
preBetaX[i].mul(&preA[i].x, &fieldBeta)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// tableGetGEFixed retrieves a point from a fixed-size table
|
||||
func tableGetGEFixed(r *GroupElementAffine, pre *[glvTableSize]GroupElementAffine, n int) {
|
||||
if n == 0 {
|
||||
r.setInfinity()
|
||||
return
|
||||
}
|
||||
|
||||
var idx int
|
||||
if n > 0 {
|
||||
idx = (n - 1) / 2
|
||||
} else {
|
||||
idx = (-n - 1) / 2
|
||||
}
|
||||
|
||||
if idx >= glvTableSize {
|
||||
r.setInfinity()
|
||||
return
|
||||
}
|
||||
|
||||
*r = pre[idx]
|
||||
|
||||
// Negate if n < 0
|
||||
if n < 0 {
|
||||
r.negate(r)
|
||||
}
|
||||
}
|
||||
|
||||
// EcmultStraussWNAFGLV is the public interface for optimized Strauss+GLV+wNAF multiplication
|
||||
func EcmultStraussWNAFGLV(r *GroupElementJacobian, a *GroupElementAffine, q *Scalar) {
|
||||
ecmultStraussWNAFGLV(r, a, q)
|
||||
}
|
||||
|
||||
// ECDHXOnly computes X-only ECDH (BIP-340 style)
|
||||
// Outputs only the X coordinate of the shared secret point
|
||||
func ECDHXOnly(output []byte, pubkey *PublicKey, seckey []byte) error {
|
||||
|
||||
425
ecmult_gen.go
425
ecmult_gen.go
@@ -1,177 +1,324 @@
|
||||
package p256k1
|
||||
|
||||
import (
|
||||
"sync"
|
||||
)
|
||||
// =============================================================================
|
||||
// Phase 5: Generator Precomputation for GLV Optimization
|
||||
// =============================================================================
|
||||
//
|
||||
// This file contains precomputed tables for the secp256k1 generator point G
|
||||
// and its λ-transformed version λ*G. These tables enable very fast scalar
|
||||
// multiplication of the generator point.
|
||||
//
|
||||
// The GLV approach splits a 256-bit scalar k into two ~128-bit scalars k1, k2
|
||||
// such that k = k1 + k2*λ (mod n). Then k*G = k1*G + k2*(λ*G).
|
||||
//
|
||||
// We precompute odd multiples of G and λ*G:
|
||||
// preGenG[i] = (2*i+1) * G for i = 0 to tableSize-1
|
||||
// preGenLambdaG[i] = (2*i+1) * (λ*G) for i = 0 to tableSize-1
|
||||
//
|
||||
// Reference: libsecp256k1 ecmult_gen_impl.h
|
||||
|
||||
const (
|
||||
// Number of bytes in a 256-bit scalar
|
||||
numBytes = 32
|
||||
// Number of possible byte values
|
||||
numByteValues = 256
|
||||
)
|
||||
|
||||
// bytePointTable stores precomputed byte points for each byte position
|
||||
// bytePoints[byteNum][byteVal] = byteVal * 2^(8*(31-byteNum)) * G
|
||||
// where byteNum is 0-31 (MSB to LSB) and byteVal is 0-255
|
||||
// Each entry stores [X, Y] coordinates as 32-byte arrays
|
||||
type bytePointTable [numBytes][numByteValues][2][32]byte
|
||||
|
||||
// EcmultGenContext holds precomputed data for generator multiplication
|
||||
type EcmultGenContext struct {
|
||||
// Precomputed byte points: bytePoints[byteNum][byteVal] = [X, Y] coordinates
|
||||
// in affine form for byteVal * 2^(8*(31-byteNum)) * G
|
||||
bytePoints bytePointTable
|
||||
initialized bool
|
||||
}
|
||||
// Window size for generator multiplication
|
||||
// Larger window = more precomputation but faster multiplication
|
||||
const genWindowSize = 6
|
||||
const genTableSize = 1 << (genWindowSize - 1) // 32 entries
|
||||
|
||||
// Precomputed tables for generator multiplication
|
||||
// These are computed once at init() time
|
||||
var (
|
||||
// Global context for generator multiplication (initialized once)
|
||||
globalGenContext *EcmultGenContext
|
||||
genContextOnce sync.Once
|
||||
// preGenG contains odd multiples of G: preGenG[i] = (2*i+1)*G
|
||||
preGenG [genTableSize]GroupElementAffine
|
||||
|
||||
// preGenLambdaG contains odd multiples of λ*G: preGenLambdaG[i] = (2*i+1)*(λ*G)
|
||||
preGenLambdaG [genTableSize]GroupElementAffine
|
||||
|
||||
// preGenBetaX contains β*x for each point in preGenG (for potential future optimization)
|
||||
preGenBetaX [genTableSize]FieldElement
|
||||
|
||||
// genTablesInitialized tracks whether the tables have been computed
|
||||
genTablesInitialized bool
|
||||
)
|
||||
|
||||
// initGenContext initializes the precomputed byte points table
|
||||
func (ctx *EcmultGenContext) initGenContext() {
|
||||
// Start with G (generator point)
|
||||
// initGenTables computes the precomputed generator tables
|
||||
// This is called automatically on first use
|
||||
func initGenTables() {
|
||||
if genTablesInitialized {
|
||||
return
|
||||
}
|
||||
|
||||
// Build odd multiples of G
|
||||
var gJac GroupElementJacobian
|
||||
gJac.setGE(&Generator)
|
||||
|
||||
// Compute base points for each byte position
|
||||
// For byteNum i, we need: byteVal * 2^(8*(31-i)) * G
|
||||
// We'll compute each byte position's base multiplier first
|
||||
var preJacG [genTableSize]GroupElementJacobian
|
||||
preJacG[0] = gJac
|
||||
|
||||
// Compute 2^8 * G, 2^16 * G, ..., 2^248 * G
|
||||
var byteBases [numBytes]GroupElementJacobian
|
||||
// Compute 2*G
|
||||
var twoG GroupElementJacobian
|
||||
twoG.double(&gJac)
|
||||
|
||||
// Base for byte 31 (LSB): 2^0 * G = G
|
||||
byteBases[31] = gJac
|
||||
// Build odd multiples: preJacG[i] = (2*i+1)*G
|
||||
for i := 1; i < genTableSize; i++ {
|
||||
preJacG[i].addVar(&preJacG[i-1], &twoG)
|
||||
}
|
||||
|
||||
// Compute bases for bytes 30 down to 0 (MSB)
|
||||
// byteBases[i] = 2^(8*(31-i)) * G
|
||||
for i := numBytes - 2; i >= 0; i-- {
|
||||
// byteBases[i] = byteBases[i+1] * 2^8
|
||||
byteBases[i] = byteBases[i+1]
|
||||
for j := 0; j < 8; j++ {
|
||||
byteBases[i].double(&byteBases[i])
|
||||
// Batch normalize to affine
|
||||
BatchNormalize(preGenG[:], preJacG[:])
|
||||
|
||||
// Compute λ*G
|
||||
var lambdaG GroupElementAffine
|
||||
lambdaG.mulLambda(&Generator)
|
||||
|
||||
// Build odd multiples of λ*G
|
||||
var lambdaGJac GroupElementJacobian
|
||||
lambdaGJac.setGE(&lambdaG)
|
||||
|
||||
var preJacLambdaG [genTableSize]GroupElementJacobian
|
||||
preJacLambdaG[0] = lambdaGJac
|
||||
|
||||
// Compute 2*(λ*G)
|
||||
var twoLambdaG GroupElementJacobian
|
||||
twoLambdaG.double(&lambdaGJac)
|
||||
|
||||
// Build odd multiples: preJacLambdaG[i] = (2*i+1)*(λ*G)
|
||||
for i := 1; i < genTableSize; i++ {
|
||||
preJacLambdaG[i].addVar(&preJacLambdaG[i-1], &twoLambdaG)
|
||||
}
|
||||
|
||||
// Batch normalize to affine
|
||||
BatchNormalize(preGenLambdaG[:], preJacLambdaG[:])
|
||||
|
||||
// Precompute β*x for each point in preGenG
|
||||
for i := 0; i < genTableSize; i++ {
|
||||
if preGenG[i].isInfinity() {
|
||||
preGenBetaX[i] = FieldElementZero
|
||||
} else {
|
||||
preGenBetaX[i].mul(&preGenG[i].x, &fieldBeta)
|
||||
}
|
||||
}
|
||||
|
||||
// Now compute all byte points for each byte position
|
||||
for byteNum := 0; byteNum < numBytes; byteNum++ {
|
||||
base := byteBases[byteNum]
|
||||
|
||||
// Convert base to affine for efficiency
|
||||
var baseAff GroupElementAffine
|
||||
baseAff.setGEJ(&base)
|
||||
|
||||
// bytePoints[byteNum][0] = infinity (point at infinity)
|
||||
// We'll skip this and handle it in the lookup
|
||||
|
||||
// bytePoints[byteNum][1] = base
|
||||
var ptJac GroupElementJacobian
|
||||
ptJac.setGE(&baseAff)
|
||||
var ptAff GroupElementAffine
|
||||
ptAff.setGEJ(&ptJac)
|
||||
ptAff.x.normalize()
|
||||
ptAff.y.normalize()
|
||||
ptAff.x.getB32(ctx.bytePoints[byteNum][1][0][:])
|
||||
ptAff.y.getB32(ctx.bytePoints[byteNum][1][1][:])
|
||||
|
||||
// Compute bytePoints[byteNum][byteVal] = byteVal * base
|
||||
// We'll use addition to build up multiples
|
||||
var accJac GroupElementJacobian = ptJac
|
||||
var accAff GroupElementAffine
|
||||
|
||||
for byteVal := 2; byteVal < numByteValues; byteVal++ {
|
||||
// acc = acc + base
|
||||
accJac.addVar(&accJac, &ptJac)
|
||||
accAff.setGEJ(&accJac)
|
||||
accAff.x.normalize()
|
||||
accAff.y.normalize()
|
||||
accAff.x.getB32(ctx.bytePoints[byteNum][byteVal][0][:])
|
||||
accAff.y.getB32(ctx.bytePoints[byteNum][byteVal][1][:])
|
||||
}
|
||||
}
|
||||
|
||||
ctx.initialized = true
|
||||
genTablesInitialized = true
|
||||
}
|
||||
|
||||
// getGlobalGenContext returns the global precomputed context
|
||||
func getGlobalGenContext() *EcmultGenContext {
|
||||
genContextOnce.Do(func() {
|
||||
globalGenContext = &EcmultGenContext{}
|
||||
globalGenContext.initGenContext()
|
||||
})
|
||||
return globalGenContext
|
||||
// EnsureGenTablesInitialized ensures the generator tables are computed
|
||||
// This is automatically called by ecmultGenGLV, but can be called explicitly
|
||||
// during application startup to avoid first-use latency
|
||||
func EnsureGenTablesInitialized() {
|
||||
initGenTables()
|
||||
}
|
||||
|
||||
// NewEcmultGenContext creates a new generator multiplication context
|
||||
func NewEcmultGenContext() *EcmultGenContext {
|
||||
ctx := &EcmultGenContext{}
|
||||
ctx.initGenContext()
|
||||
return ctx
|
||||
}
|
||||
|
||||
// ecmultGen computes r = n * G where G is the generator point
|
||||
// Uses 8-bit byte-based lookup table (like btcec) for maximum efficiency
|
||||
func (ctx *EcmultGenContext) ecmultGen(r *GroupElementJacobian, n *Scalar) {
|
||||
if !ctx.initialized {
|
||||
panic("ecmult_gen context not initialized")
|
||||
}
|
||||
|
||||
// Handle zero scalar
|
||||
if n.isZero() {
|
||||
// ecmultGenGLV computes r = k * G using precomputed tables and GLV endomorphism
|
||||
// This is the fastest method for generator multiplication
|
||||
func ecmultGenGLV(r *GroupElementJacobian, k *Scalar) {
|
||||
if k.isZero() {
|
||||
r.setInfinity()
|
||||
return
|
||||
}
|
||||
|
||||
// Handle scalar = 1
|
||||
if n.isOne() {
|
||||
r.setGE(&Generator)
|
||||
// Ensure tables are initialized
|
||||
initGenTables()
|
||||
|
||||
// Split scalar using GLV: k = k1 + k2*λ
|
||||
var k1, k2 Scalar
|
||||
scalarSplitLambda(&k1, &k2, k)
|
||||
|
||||
// Normalize k1 and k2 to be "low" (not high)
|
||||
// If k1 is high, negate it and we'll negate the final contribution
|
||||
neg1 := k1.isHigh()
|
||||
if neg1 {
|
||||
k1.negate(&k1)
|
||||
}
|
||||
|
||||
neg2 := k2.isHigh()
|
||||
if neg2 {
|
||||
k2.negate(&k2)
|
||||
}
|
||||
|
||||
// Convert to wNAF
|
||||
const wnafMaxLen = 257
|
||||
var wnaf1, wnaf2 [wnafMaxLen]int
|
||||
|
||||
bits1 := k1.wNAF(wnaf1[:], genWindowSize)
|
||||
bits2 := k2.wNAF(wnaf2[:], genWindowSize)
|
||||
|
||||
// Find maximum bit position
|
||||
maxBits := bits1
|
||||
if bits2 > maxBits {
|
||||
maxBits = bits2
|
||||
}
|
||||
|
||||
// Perform Strauss algorithm using precomputed tables
|
||||
r.setInfinity()
|
||||
|
||||
for i := maxBits - 1; i >= 0; i-- {
|
||||
// Double the result
|
||||
if !r.isInfinity() {
|
||||
r.double(r)
|
||||
}
|
||||
|
||||
// Add contribution from k1 (using preGenG table)
|
||||
if i < bits1 && wnaf1[i] != 0 {
|
||||
var pt GroupElementAffine
|
||||
n := wnaf1[i]
|
||||
|
||||
var idx int
|
||||
if n > 0 {
|
||||
idx = (n - 1) / 2
|
||||
} else {
|
||||
idx = (-n - 1) / 2
|
||||
}
|
||||
|
||||
if idx < genTableSize {
|
||||
pt = preGenG[idx]
|
||||
// Negate if wNAF digit is negative
|
||||
if n < 0 {
|
||||
pt.negate(&pt)
|
||||
}
|
||||
// Negate if k1 was negated during normalization
|
||||
if neg1 {
|
||||
pt.negate(&pt)
|
||||
}
|
||||
|
||||
if r.isInfinity() {
|
||||
r.setGE(&pt)
|
||||
} else {
|
||||
r.addGE(r, &pt)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Add contribution from k2 (using preGenLambdaG table)
|
||||
if i < bits2 && wnaf2[i] != 0 {
|
||||
var pt GroupElementAffine
|
||||
n := wnaf2[i]
|
||||
|
||||
var idx int
|
||||
if n > 0 {
|
||||
idx = (n - 1) / 2
|
||||
} else {
|
||||
idx = (-n - 1) / 2
|
||||
}
|
||||
|
||||
if idx < genTableSize {
|
||||
pt = preGenLambdaG[idx]
|
||||
// Negate if wNAF digit is negative
|
||||
if n < 0 {
|
||||
pt.negate(&pt)
|
||||
}
|
||||
// Negate if k2 was negated during normalization
|
||||
if neg2 {
|
||||
pt.negate(&pt)
|
||||
}
|
||||
|
||||
if r.isInfinity() {
|
||||
r.setGE(&pt)
|
||||
} else {
|
||||
r.addGE(r, &pt)
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// EcmultGenGLV is the public interface for fast generator multiplication
|
||||
// r = k * G
|
||||
func EcmultGenGLV(r *GroupElementJacobian, k *Scalar) {
|
||||
ecmultGenGLV(r, k)
|
||||
}
|
||||
|
||||
// ecmultGenSimple computes r = k * G using a simple approach without GLV
|
||||
// This uses the precomputed table for G only, without scalar splitting
|
||||
// Useful for comparison and as a fallback
|
||||
func ecmultGenSimple(r *GroupElementJacobian, k *Scalar) {
|
||||
if k.isZero() {
|
||||
r.setInfinity()
|
||||
return
|
||||
}
|
||||
|
||||
// Byte-based method: process one byte at a time (MSB to LSB)
|
||||
// For each byte, lookup the precomputed point and add it
|
||||
// Ensure tables are initialized
|
||||
initGenTables()
|
||||
|
||||
// Normalize scalar if it's high (has high bit set)
|
||||
var kNorm Scalar
|
||||
kNorm = *k
|
||||
negResult := kNorm.isHigh()
|
||||
if negResult {
|
||||
kNorm.negate(&kNorm)
|
||||
}
|
||||
|
||||
// Convert to wNAF
|
||||
const wnafMaxLen = 257
|
||||
var wnaf [wnafMaxLen]int
|
||||
|
||||
bits := kNorm.wNAF(wnaf[:], genWindowSize)
|
||||
|
||||
// Perform algorithm using precomputed table
|
||||
r.setInfinity()
|
||||
|
||||
// Get scalar bytes (MSB to LSB) - optimize by getting bytes directly
|
||||
var scalarBytes [32]byte
|
||||
n.getB32(scalarBytes[:])
|
||||
|
||||
// Pre-allocate group elements to avoid repeated allocations
|
||||
var ptAff GroupElementAffine
|
||||
var ptJac GroupElementJacobian
|
||||
var xFe, yFe FieldElement
|
||||
|
||||
for byteNum := 0; byteNum < numBytes; byteNum++ {
|
||||
byteVal := scalarBytes[byteNum]
|
||||
|
||||
// Skip zero bytes
|
||||
if byteVal == 0 {
|
||||
continue
|
||||
for i := bits - 1; i >= 0; i-- {
|
||||
// Double the result
|
||||
if !r.isInfinity() {
|
||||
r.double(r)
|
||||
}
|
||||
|
||||
// Lookup precomputed point for this byte - optimized: reuse field elements
|
||||
xFe.setB32(ctx.bytePoints[byteNum][byteVal][0][:])
|
||||
yFe.setB32(ctx.bytePoints[byteNum][byteVal][1][:])
|
||||
ptAff.setXY(&xFe, &yFe)
|
||||
// Add contribution
|
||||
if wnaf[i] != 0 {
|
||||
var pt GroupElementAffine
|
||||
n := wnaf[i]
|
||||
|
||||
// Convert to Jacobian and add - optimized: reuse Jacobian element
|
||||
ptJac.setGE(&ptAff)
|
||||
var idx int
|
||||
if n > 0 {
|
||||
idx = (n - 1) / 2
|
||||
} else {
|
||||
idx = (-n - 1) / 2
|
||||
}
|
||||
|
||||
if r.isInfinity() {
|
||||
*r = ptJac
|
||||
} else {
|
||||
r.addVar(r, &ptJac)
|
||||
if idx < genTableSize {
|
||||
pt = preGenG[idx]
|
||||
if n < 0 {
|
||||
pt.negate(&pt)
|
||||
}
|
||||
|
||||
if r.isInfinity() {
|
||||
r.setGE(&pt)
|
||||
} else {
|
||||
r.addGE(r, &pt)
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Negate result if we negated the scalar
|
||||
if negResult {
|
||||
r.negate(r)
|
||||
}
|
||||
}
|
||||
|
||||
// EcmultGen is the public interface for generator multiplication
|
||||
func EcmultGen(r *GroupElementJacobian, n *Scalar) {
|
||||
// Use global precomputed context for efficiency
|
||||
ctx := getGlobalGenContext()
|
||||
ctx.ecmultGen(r, n)
|
||||
// EcmultGenSimple is the public interface for simple generator multiplication
|
||||
func EcmultGenSimple(r *GroupElementJacobian, k *Scalar) {
|
||||
ecmultGenSimple(r, k)
|
||||
}
|
||||
|
||||
// =============================================================================
|
||||
// EcmultGenContext - Compatibility layer for existing codebase
|
||||
// =============================================================================
|
||||
|
||||
// EcmultGenContext represents the generator multiplication context
|
||||
// This wraps the precomputed tables for generator multiplication
|
||||
type EcmultGenContext struct {
|
||||
initialized bool
|
||||
}
|
||||
|
||||
// NewEcmultGenContext creates a new generator multiplication context
|
||||
// This initializes the precomputed tables if not already done
|
||||
func NewEcmultGenContext() *EcmultGenContext {
|
||||
initGenTables()
|
||||
return &EcmultGenContext{
|
||||
initialized: true,
|
||||
}
|
||||
}
|
||||
|
||||
// EcmultGen computes r = k * G using the fastest available method
|
||||
// This is the main entry point for generator multiplication throughout the codebase
|
||||
func EcmultGen(r *GroupElementJacobian, k *Scalar) {
|
||||
ecmultGenGLV(r, k)
|
||||
}
|
||||
|
||||
16
field.go
16
field.go
@@ -59,6 +59,22 @@ var (
|
||||
normalized: true,
|
||||
}
|
||||
|
||||
// fieldBeta is the GLV endomorphism constant β (cube root of unity mod p)
|
||||
// β^3 ≡ 1 (mod p), and β^2 + β + 1 ≡ 0 (mod p)
|
||||
// This enables the endomorphism: λ·(x,y) = (β·x, y) on secp256k1
|
||||
// Value: 0x7ae96a2b657c07106e64479eac3434e99cf0497512f58995c1396c28719501ee
|
||||
// From libsecp256k1 field.h lines 67-70
|
||||
fieldBeta = FieldElement{
|
||||
n: [5]uint64{
|
||||
0x96c28719501ee, // limb 0 (52 bits)
|
||||
0x7512f58995c13, // limb 1 (52 bits)
|
||||
0xc3434e99cf049, // limb 2 (52 bits)
|
||||
0x7106e64479ea, // limb 3 (52 bits)
|
||||
0x7ae96a2b657c, // limb 4 (48 bits)
|
||||
},
|
||||
magnitude: 1,
|
||||
normalized: true,
|
||||
}
|
||||
)
|
||||
|
||||
func NewFieldElement() *FieldElement {
|
||||
|
||||
@@ -16,8 +16,26 @@ func fieldMulAsm(r, a, b *FieldElement)
|
||||
//go:noescape
|
||||
func fieldSqrAsm(r, a *FieldElement)
|
||||
|
||||
// fieldMulAsmBMI2 multiplies two field elements using BMI2+ADX instructions.
|
||||
// Uses MULX for flag-free multiplication enabling parallel carry chains.
|
||||
// r, a, b are 5x52-bit limb representations.
|
||||
//
|
||||
//go:noescape
|
||||
func fieldMulAsmBMI2(r, a, b *FieldElement)
|
||||
|
||||
// fieldSqrAsmBMI2 squares a field element using BMI2+ADX instructions.
|
||||
// Uses MULX for flag-free multiplication.
|
||||
//
|
||||
//go:noescape
|
||||
func fieldSqrAsmBMI2(r, a *FieldElement)
|
||||
|
||||
// hasFieldAsm returns true if field assembly is available.
|
||||
// On amd64, this is always true.
|
||||
func hasFieldAsm() bool {
|
||||
return true
|
||||
}
|
||||
|
||||
// hasFieldAsmBMI2 returns true if BMI2+ADX optimized field assembly is available.
|
||||
func hasFieldAsmBMI2() bool {
|
||||
return HasBMI2()
|
||||
}
|
||||
|
||||
771
field_amd64_bmi2.s
Normal file
771
field_amd64_bmi2.s
Normal file
@@ -0,0 +1,771 @@
|
||||
//go:build amd64
|
||||
|
||||
#include "textflag.h"
|
||||
|
||||
// Field multiplication assembly for secp256k1 using BMI2+ADX instructions.
|
||||
// Uses MULX for flag-free multiplication and ADCX/ADOX for parallel carry chains.
|
||||
//
|
||||
// The field element is represented as 5 limbs of 52 bits each:
|
||||
// n[0..4] where value = sum(n[i] * 2^(52*i))
|
||||
//
|
||||
// Field prime p = 2^256 - 2^32 - 977
|
||||
// Reduction constant R = 2^256 mod p = 2^32 + 977 = 0x1000003D1
|
||||
// For 5x52: R shifted = 0x1000003D10 (for 52-bit alignment)
|
||||
//
|
||||
// BMI2 Instructions used:
|
||||
// MULXQ src, lo, hi - unsigned multiply RDX * src -> hi:lo (flags unchanged)
|
||||
//
|
||||
// ADX Instructions used:
|
||||
// ADCXQ src, dst - dst += src + CF (only modifies CF)
|
||||
// ADOXQ src, dst - dst += src + OF (only modifies OF)
|
||||
//
|
||||
// ADCX/ADOX allow parallel carry chains: ADCX uses CF only, ADOX uses OF only.
|
||||
// This enables the CPU to execute two independent addition chains in parallel.
|
||||
//
|
||||
// Stack layout for fieldMulAsmBMI2 (96 bytes):
|
||||
// 0(SP) - d_lo
|
||||
// 8(SP) - d_hi
|
||||
// 16(SP) - c_lo
|
||||
// 24(SP) - c_hi
|
||||
// 32(SP) - t3
|
||||
// 40(SP) - t4
|
||||
// 48(SP) - tx
|
||||
// 56(SP) - u0
|
||||
// 64(SP) - temp storage
|
||||
// 72(SP) - temp storage 2
|
||||
// 80(SP) - saved b pointer
|
||||
|
||||
// func fieldMulAsmBMI2(r, a, b *FieldElement)
|
||||
TEXT ·fieldMulAsmBMI2(SB), NOSPLIT, $96-24
|
||||
MOVQ r+0(FP), DI
|
||||
MOVQ a+8(FP), SI
|
||||
MOVQ b+16(FP), BX
|
||||
|
||||
// Save b pointer
|
||||
MOVQ BX, 80(SP)
|
||||
|
||||
// Load a[0..4] into registers
|
||||
MOVQ 0(SI), R8 // a0
|
||||
MOVQ 8(SI), R9 // a1
|
||||
MOVQ 16(SI), R10 // a2
|
||||
MOVQ 24(SI), R11 // a3
|
||||
MOVQ 32(SI), R12 // a4
|
||||
|
||||
// Constants:
|
||||
// M = 0xFFFFFFFFFFFFF (2^52 - 1)
|
||||
// R = 0x1000003D10
|
||||
|
||||
// === Step 1: d = a0*b3 + a1*b2 + a2*b1 + a3*b0 ===
|
||||
// Using MULX: put multiplier in RDX, result in specified regs
|
||||
MOVQ 24(BX), DX // b3
|
||||
MULXQ R8, AX, CX // a0 * b3 -> CX:AX
|
||||
MOVQ AX, 0(SP) // d_lo
|
||||
MOVQ CX, 8(SP) // d_hi
|
||||
|
||||
MOVQ 16(BX), DX // b2
|
||||
MULXQ R9, AX, CX // a1 * b2 -> CX:AX
|
||||
ADDQ AX, 0(SP)
|
||||
ADCQ CX, 8(SP)
|
||||
|
||||
MOVQ 8(BX), DX // b1
|
||||
MULXQ R10, AX, CX // a2 * b1 -> CX:AX
|
||||
ADDQ AX, 0(SP)
|
||||
ADCQ CX, 8(SP)
|
||||
|
||||
MOVQ 0(BX), DX // b0
|
||||
MULXQ R11, AX, CX // a3 * b0 -> CX:AX
|
||||
ADDQ AX, 0(SP)
|
||||
ADCQ CX, 8(SP)
|
||||
|
||||
// === Step 2: c = a4*b4 ===
|
||||
MOVQ 32(BX), DX // b4
|
||||
MULXQ R12, AX, CX // a4 * b4 -> CX:AX
|
||||
MOVQ AX, 16(SP) // c_lo
|
||||
MOVQ CX, 24(SP) // c_hi
|
||||
|
||||
// === Step 3: d += R * c_lo ===
|
||||
MOVQ 16(SP), DX // c_lo
|
||||
MOVQ $0x1000003D10, R13 // R constant
|
||||
MULXQ R13, AX, CX // R * c_lo -> CX:AX
|
||||
ADDQ AX, 0(SP)
|
||||
ADCQ CX, 8(SP)
|
||||
|
||||
// === Step 4: c >>= 64 ===
|
||||
MOVQ 24(SP), AX
|
||||
MOVQ AX, 16(SP)
|
||||
MOVQ $0, 24(SP)
|
||||
|
||||
// === Step 5: t3 = d & M; d >>= 52 ===
|
||||
MOVQ 0(SP), AX
|
||||
MOVQ $0xFFFFFFFFFFFFF, R14 // M constant (keep in register)
|
||||
ANDQ R14, AX
|
||||
MOVQ AX, 32(SP) // t3
|
||||
|
||||
MOVQ 0(SP), AX
|
||||
MOVQ 8(SP), CX
|
||||
SHRQ $52, AX
|
||||
MOVQ CX, DX
|
||||
SHLQ $12, DX
|
||||
ORQ DX, AX
|
||||
SHRQ $52, CX
|
||||
MOVQ AX, 0(SP)
|
||||
MOVQ CX, 8(SP)
|
||||
|
||||
// === Step 6: d += a0*b4 + a1*b3 + a2*b2 + a3*b1 + a4*b0 ===
|
||||
MOVQ 80(SP), BX // restore b pointer
|
||||
|
||||
MOVQ 32(BX), DX // b4
|
||||
MULXQ R8, AX, CX // a0 * b4
|
||||
ADDQ AX, 0(SP)
|
||||
ADCQ CX, 8(SP)
|
||||
|
||||
MOVQ 24(BX), DX // b3
|
||||
MULXQ R9, AX, CX // a1 * b3
|
||||
ADDQ AX, 0(SP)
|
||||
ADCQ CX, 8(SP)
|
||||
|
||||
MOVQ 16(BX), DX // b2
|
||||
MULXQ R10, AX, CX // a2 * b2
|
||||
ADDQ AX, 0(SP)
|
||||
ADCQ CX, 8(SP)
|
||||
|
||||
MOVQ 8(BX), DX // b1
|
||||
MULXQ R11, AX, CX // a3 * b1
|
||||
ADDQ AX, 0(SP)
|
||||
ADCQ CX, 8(SP)
|
||||
|
||||
MOVQ 0(BX), DX // b0
|
||||
MULXQ R12, AX, CX // a4 * b0
|
||||
ADDQ AX, 0(SP)
|
||||
ADCQ CX, 8(SP)
|
||||
|
||||
// === Step 7: d += (R << 12) * c ===
|
||||
MOVQ 16(SP), DX // c
|
||||
MOVQ $0x1000003D10000, R15 // R << 12
|
||||
MULXQ R15, AX, CX
|
||||
ADDQ AX, 0(SP)
|
||||
ADCQ CX, 8(SP)
|
||||
|
||||
// === Step 8: t4 = d & M; tx = t4 >> 48; t4 &= (M >> 4) ===
|
||||
MOVQ 0(SP), AX
|
||||
ANDQ R14, AX // t4 = d & M
|
||||
MOVQ AX, 40(SP)
|
||||
|
||||
SHRQ $48, AX
|
||||
MOVQ AX, 48(SP) // tx
|
||||
|
||||
MOVQ 40(SP), AX
|
||||
MOVQ $0x0FFFFFFFFFFFF, CX
|
||||
ANDQ CX, AX
|
||||
MOVQ AX, 40(SP) // t4
|
||||
|
||||
// === Step 9: d >>= 52 ===
|
||||
MOVQ 0(SP), AX
|
||||
MOVQ 8(SP), CX
|
||||
SHRQ $52, AX
|
||||
MOVQ CX, DX
|
||||
SHLQ $12, DX
|
||||
ORQ DX, AX
|
||||
SHRQ $52, CX
|
||||
MOVQ AX, 0(SP)
|
||||
MOVQ CX, 8(SP)
|
||||
|
||||
// === Step 10: c = a0*b0 ===
|
||||
MOVQ 0(BX), DX // b0
|
||||
MULXQ R8, AX, CX // a0 * b0
|
||||
MOVQ AX, 16(SP)
|
||||
MOVQ CX, 24(SP)
|
||||
|
||||
// === Step 11: d += a1*b4 + a2*b3 + a3*b2 + a4*b1 ===
|
||||
MOVQ 32(BX), DX // b4
|
||||
MULXQ R9, AX, CX // a1 * b4
|
||||
ADDQ AX, 0(SP)
|
||||
ADCQ CX, 8(SP)
|
||||
|
||||
MOVQ 24(BX), DX // b3
|
||||
MULXQ R10, AX, CX // a2 * b3
|
||||
ADDQ AX, 0(SP)
|
||||
ADCQ CX, 8(SP)
|
||||
|
||||
MOVQ 16(BX), DX // b2
|
||||
MULXQ R11, AX, CX // a3 * b2
|
||||
ADDQ AX, 0(SP)
|
||||
ADCQ CX, 8(SP)
|
||||
|
||||
MOVQ 8(BX), DX // b1
|
||||
MULXQ R12, AX, CX // a4 * b1
|
||||
ADDQ AX, 0(SP)
|
||||
ADCQ CX, 8(SP)
|
||||
|
||||
// === Step 12: u0 = d & M; d >>= 52; u0 = (u0 << 4) | tx ===
|
||||
MOVQ 0(SP), AX
|
||||
ANDQ R14, AX // u0 = d & M
|
||||
SHLQ $4, AX
|
||||
ORQ 48(SP), AX
|
||||
MOVQ AX, 56(SP) // u0
|
||||
|
||||
MOVQ 0(SP), AX
|
||||
MOVQ 8(SP), CX
|
||||
SHRQ $52, AX
|
||||
MOVQ CX, DX
|
||||
SHLQ $12, DX
|
||||
ORQ DX, AX
|
||||
SHRQ $52, CX
|
||||
MOVQ AX, 0(SP)
|
||||
MOVQ CX, 8(SP)
|
||||
|
||||
// === Step 13: c += (R >> 4) * u0 ===
|
||||
MOVQ 56(SP), DX // u0
|
||||
MOVQ $0x1000003D1, R13 // R >> 4
|
||||
MULXQ R13, AX, CX
|
||||
ADDQ AX, 16(SP)
|
||||
ADCQ CX, 24(SP)
|
||||
|
||||
// === Step 14: r[0] = c & M; c >>= 52 ===
|
||||
MOVQ 16(SP), AX
|
||||
ANDQ R14, AX
|
||||
MOVQ AX, 0(DI) // store r[0]
|
||||
|
||||
MOVQ 16(SP), AX
|
||||
MOVQ 24(SP), CX
|
||||
SHRQ $52, AX
|
||||
MOVQ CX, DX
|
||||
SHLQ $12, DX
|
||||
ORQ DX, AX
|
||||
SHRQ $52, CX
|
||||
MOVQ AX, 16(SP)
|
||||
MOVQ CX, 24(SP)
|
||||
|
||||
// === Steps 15-16: Parallel c and d updates using ADCX/ADOX ===
|
||||
// Step 15: c += a0*b1 + a1*b0 (CF chain via ADCX)
|
||||
// Step 16: d += a2*b4 + a3*b3 + a4*b2 (OF chain via ADOX)
|
||||
// Save r pointer before reusing DI
|
||||
MOVQ DI, 64(SP) // save r pointer
|
||||
|
||||
// Load all accumulators into registers for ADCX/ADOX (register-only ops)
|
||||
MOVQ 16(SP), R13 // c_lo
|
||||
MOVQ 24(SP), R15 // c_hi
|
||||
MOVQ 0(SP), SI // d_lo (reuse SI since we don't need 'a' anymore)
|
||||
MOVQ 8(SP), DI // d_hi (reuse DI)
|
||||
|
||||
// Clear CF and OF
|
||||
XORQ AX, AX
|
||||
|
||||
// First pair: c += a0*b1, d += a2*b4
|
||||
MOVQ 8(BX), DX // b1
|
||||
MULXQ R8, AX, CX // a0 * b1 -> CX:AX
|
||||
ADCXQ AX, R13 // c_lo += lo (CF chain)
|
||||
ADCXQ CX, R15 // c_hi += hi + CF
|
||||
|
||||
MOVQ 32(BX), DX // b4
|
||||
MULXQ R10, AX, CX // a2 * b4 -> CX:AX
|
||||
ADOXQ AX, SI // d_lo += lo (OF chain)
|
||||
ADOXQ CX, DI // d_hi += hi + OF
|
||||
|
||||
// Second pair: c += a1*b0, d += a3*b3
|
||||
MOVQ 0(BX), DX // b0
|
||||
MULXQ R9, AX, CX // a1 * b0 -> CX:AX
|
||||
ADCXQ AX, R13 // c_lo += lo
|
||||
ADCXQ CX, R15 // c_hi += hi + CF
|
||||
|
||||
MOVQ 24(BX), DX // b3
|
||||
MULXQ R11, AX, CX // a3 * b3 -> CX:AX
|
||||
ADOXQ AX, SI // d_lo += lo
|
||||
ADOXQ CX, DI // d_hi += hi + OF
|
||||
|
||||
// Third: d += a4*b2 (only d, no more c operations)
|
||||
MOVQ 16(BX), DX // b2
|
||||
MULXQ R12, AX, CX // a4 * b2 -> CX:AX
|
||||
ADOXQ AX, SI // d_lo += lo
|
||||
ADOXQ CX, DI // d_hi += hi + OF
|
||||
|
||||
// Store results back
|
||||
MOVQ R13, 16(SP) // c_lo
|
||||
MOVQ R15, 24(SP) // c_hi
|
||||
MOVQ SI, 0(SP) // d_lo
|
||||
MOVQ DI, 8(SP) // d_hi
|
||||
MOVQ 64(SP), DI // restore r pointer
|
||||
|
||||
// === Step 17: c += R * (d & M); d >>= 52 ===
|
||||
MOVQ 0(SP), AX
|
||||
ANDQ R14, AX // d & M
|
||||
MOVQ AX, DX
|
||||
MOVQ $0x1000003D10, R13 // R
|
||||
MULXQ R13, AX, CX
|
||||
ADDQ AX, 16(SP)
|
||||
ADCQ CX, 24(SP)
|
||||
|
||||
MOVQ 0(SP), AX
|
||||
MOVQ 8(SP), CX
|
||||
SHRQ $52, AX
|
||||
MOVQ CX, DX
|
||||
SHLQ $12, DX
|
||||
ORQ DX, AX
|
||||
SHRQ $52, CX
|
||||
MOVQ AX, 0(SP)
|
||||
MOVQ CX, 8(SP)
|
||||
|
||||
// === Step 18: r[1] = c & M; c >>= 52 ===
|
||||
MOVQ 16(SP), AX
|
||||
ANDQ R14, AX
|
||||
MOVQ AX, 8(DI) // store r[1]
|
||||
|
||||
MOVQ 16(SP), AX
|
||||
MOVQ 24(SP), CX
|
||||
SHRQ $52, AX
|
||||
MOVQ CX, DX
|
||||
SHLQ $12, DX
|
||||
ORQ DX, AX
|
||||
SHRQ $52, CX
|
||||
MOVQ AX, 16(SP)
|
||||
MOVQ CX, 24(SP)
|
||||
|
||||
// === Steps 19-20: Parallel c and d updates using ADCX/ADOX ===
|
||||
// Step 19: c += a0*b2 + a1*b1 + a2*b0 (CF chain via ADCX)
|
||||
// Step 20: d += a3*b4 + a4*b3 (OF chain via ADOX)
|
||||
// Save r pointer before reusing DI
|
||||
MOVQ DI, 64(SP) // save r pointer
|
||||
|
||||
// Load all accumulators into registers
|
||||
MOVQ 16(SP), R13 // c_lo
|
||||
MOVQ 24(SP), R15 // c_hi
|
||||
MOVQ 0(SP), SI // d_lo
|
||||
MOVQ 8(SP), DI // d_hi
|
||||
|
||||
// Clear CF and OF
|
||||
XORQ AX, AX
|
||||
|
||||
// First pair: c += a0*b2, d += a3*b4
|
||||
MOVQ 16(BX), DX // b2
|
||||
MULXQ R8, AX, CX // a0 * b2 -> CX:AX
|
||||
ADCXQ AX, R13 // c_lo += lo
|
||||
ADCXQ CX, R15 // c_hi += hi + CF
|
||||
|
||||
MOVQ 32(BX), DX // b4
|
||||
MULXQ R11, AX, CX // a3 * b4 -> CX:AX
|
||||
ADOXQ AX, SI // d_lo += lo
|
||||
ADOXQ CX, DI // d_hi += hi + OF
|
||||
|
||||
// Second pair: c += a1*b1, d += a4*b3
|
||||
MOVQ 8(BX), DX // b1
|
||||
MULXQ R9, AX, CX // a1 * b1 -> CX:AX
|
||||
ADCXQ AX, R13 // c_lo += lo
|
||||
ADCXQ CX, R15 // c_hi += hi + CF
|
||||
|
||||
MOVQ 24(BX), DX // b3
|
||||
MULXQ R12, AX, CX // a4 * b3 -> CX:AX
|
||||
ADOXQ AX, SI // d_lo += lo
|
||||
ADOXQ CX, DI // d_hi += hi + OF
|
||||
|
||||
// Third: c += a2*b0 (only c, no more d operations)
|
||||
MOVQ 0(BX), DX // b0
|
||||
MULXQ R10, AX, CX // a2 * b0 -> CX:AX
|
||||
ADCXQ AX, R13 // c_lo += lo
|
||||
ADCXQ CX, R15 // c_hi += hi + CF
|
||||
|
||||
// Store results back
|
||||
MOVQ R13, 16(SP) // c_lo
|
||||
MOVQ R15, 24(SP) // c_hi
|
||||
MOVQ SI, 0(SP) // d_lo
|
||||
MOVQ DI, 8(SP) // d_hi
|
||||
MOVQ 64(SP), DI // restore r pointer
|
||||
|
||||
// === Step 21: c += R * d_lo; d >>= 64 ===
|
||||
MOVQ 0(SP), DX // d_lo
|
||||
MOVQ $0x1000003D10, R13 // R
|
||||
MULXQ R13, AX, CX
|
||||
ADDQ AX, 16(SP)
|
||||
ADCQ CX, 24(SP)
|
||||
|
||||
MOVQ 8(SP), AX
|
||||
MOVQ AX, 0(SP)
|
||||
MOVQ $0, 8(SP)
|
||||
|
||||
// === Step 22: r[2] = c & M; c >>= 52 ===
|
||||
MOVQ 16(SP), AX
|
||||
ANDQ R14, AX
|
||||
MOVQ AX, 16(DI) // store r[2]
|
||||
|
||||
MOVQ 16(SP), AX
|
||||
MOVQ 24(SP), CX
|
||||
SHRQ $52, AX
|
||||
MOVQ CX, DX
|
||||
SHLQ $12, DX
|
||||
ORQ DX, AX
|
||||
SHRQ $52, CX
|
||||
MOVQ AX, 16(SP)
|
||||
MOVQ CX, 24(SP)
|
||||
|
||||
// === Step 23: c += (R << 12) * d + t3 ===
|
||||
MOVQ 0(SP), DX // d
|
||||
MOVQ $0x1000003D10000, R15 // R << 12 (reload since R15 was used for c_hi)
|
||||
MULXQ R15, AX, CX // (R << 12) * d
|
||||
ADDQ AX, 16(SP)
|
||||
ADCQ CX, 24(SP)
|
||||
|
||||
MOVQ 32(SP), AX // t3
|
||||
ADDQ AX, 16(SP)
|
||||
ADCQ $0, 24(SP)
|
||||
|
||||
// === Step 24: r[3] = c & M; c >>= 52 ===
|
||||
MOVQ 16(SP), AX
|
||||
ANDQ R14, AX
|
||||
MOVQ AX, 24(DI) // store r[3]
|
||||
|
||||
MOVQ 16(SP), AX
|
||||
MOVQ 24(SP), CX
|
||||
SHRQ $52, AX
|
||||
MOVQ CX, DX
|
||||
SHLQ $12, DX
|
||||
ORQ DX, AX
|
||||
|
||||
// === Step 25: r[4] = c + t4 ===
|
||||
ADDQ 40(SP), AX
|
||||
MOVQ AX, 32(DI) // store r[4]
|
||||
|
||||
RET
|
||||
|
||||
|
||||
// func fieldSqrAsmBMI2(r, a *FieldElement)
|
||||
// Squares a field element using BMI2 instructions.
|
||||
TEXT ·fieldSqrAsmBMI2(SB), NOSPLIT, $96-16
|
||||
MOVQ r+0(FP), DI
|
||||
MOVQ a+8(FP), SI
|
||||
|
||||
// Load a[0..4] into registers
|
||||
MOVQ 0(SI), R8 // a0
|
||||
MOVQ 8(SI), R9 // a1
|
||||
MOVQ 16(SI), R10 // a2
|
||||
MOVQ 24(SI), R11 // a3
|
||||
MOVQ 32(SI), R12 // a4
|
||||
|
||||
// Keep M constant in R14
|
||||
MOVQ $0xFFFFFFFFFFFFF, R14
|
||||
|
||||
// === Step 1: d = 2*a0*a3 + 2*a1*a2 ===
|
||||
MOVQ R8, DX
|
||||
ADDQ DX, DX // 2*a0
|
||||
MULXQ R11, AX, CX // 2*a0 * a3
|
||||
MOVQ AX, 0(SP)
|
||||
MOVQ CX, 8(SP)
|
||||
|
||||
MOVQ R9, DX
|
||||
ADDQ DX, DX // 2*a1
|
||||
MULXQ R10, AX, CX // 2*a1 * a2
|
||||
ADDQ AX, 0(SP)
|
||||
ADCQ CX, 8(SP)
|
||||
|
||||
// === Step 2: c = a4*a4 ===
|
||||
MOVQ R12, DX
|
||||
MULXQ R12, AX, CX // a4 * a4
|
||||
MOVQ AX, 16(SP)
|
||||
MOVQ CX, 24(SP)
|
||||
|
||||
// === Step 3: d += R * c_lo ===
|
||||
MOVQ 16(SP), DX
|
||||
MOVQ $0x1000003D10, R13
|
||||
MULXQ R13, AX, CX
|
||||
ADDQ AX, 0(SP)
|
||||
ADCQ CX, 8(SP)
|
||||
|
||||
// === Step 4: c >>= 64 ===
|
||||
MOVQ 24(SP), AX
|
||||
MOVQ AX, 16(SP)
|
||||
MOVQ $0, 24(SP)
|
||||
|
||||
// === Step 5: t3 = d & M; d >>= 52 ===
|
||||
MOVQ 0(SP), AX
|
||||
ANDQ R14, AX
|
||||
MOVQ AX, 32(SP) // t3
|
||||
|
||||
MOVQ 0(SP), AX
|
||||
MOVQ 8(SP), CX
|
||||
SHRQ $52, AX
|
||||
MOVQ CX, DX
|
||||
SHLQ $12, DX
|
||||
ORQ DX, AX
|
||||
SHRQ $52, CX
|
||||
MOVQ AX, 0(SP)
|
||||
MOVQ CX, 8(SP)
|
||||
|
||||
// === Step 6: d += 2*a0*a4 + 2*a1*a3 + a2*a2 ===
|
||||
// Pre-compute 2*a4
|
||||
MOVQ R12, R15
|
||||
ADDQ R15, R15 // 2*a4
|
||||
|
||||
MOVQ R8, DX
|
||||
MULXQ R15, AX, CX // a0 * 2*a4
|
||||
ADDQ AX, 0(SP)
|
||||
ADCQ CX, 8(SP)
|
||||
|
||||
MOVQ R9, DX
|
||||
ADDQ DX, DX // 2*a1
|
||||
MULXQ R11, AX, CX // 2*a1 * a3
|
||||
ADDQ AX, 0(SP)
|
||||
ADCQ CX, 8(SP)
|
||||
|
||||
MOVQ R10, DX
|
||||
MULXQ R10, AX, CX // a2 * a2
|
||||
ADDQ AX, 0(SP)
|
||||
ADCQ CX, 8(SP)
|
||||
|
||||
// === Step 7: d += (R << 12) * c ===
|
||||
MOVQ 16(SP), DX
|
||||
MOVQ $0x1000003D10000, R13
|
||||
MULXQ R13, AX, CX
|
||||
ADDQ AX, 0(SP)
|
||||
ADCQ CX, 8(SP)
|
||||
|
||||
// === Step 8: t4 = d & M; tx = t4 >> 48; t4 &= (M >> 4) ===
|
||||
MOVQ 0(SP), AX
|
||||
ANDQ R14, AX
|
||||
MOVQ AX, 40(SP)
|
||||
|
||||
SHRQ $48, AX
|
||||
MOVQ AX, 48(SP) // tx
|
||||
|
||||
MOVQ 40(SP), AX
|
||||
MOVQ $0x0FFFFFFFFFFFF, CX
|
||||
ANDQ CX, AX
|
||||
MOVQ AX, 40(SP) // t4
|
||||
|
||||
// === Step 9: d >>= 52 ===
|
||||
MOVQ 0(SP), AX
|
||||
MOVQ 8(SP), CX
|
||||
SHRQ $52, AX
|
||||
MOVQ CX, DX
|
||||
SHLQ $12, DX
|
||||
ORQ DX, AX
|
||||
SHRQ $52, CX
|
||||
MOVQ AX, 0(SP)
|
||||
MOVQ CX, 8(SP)
|
||||
|
||||
// === Step 10: c = a0*a0 ===
|
||||
MOVQ R8, DX
|
||||
MULXQ R8, AX, CX
|
||||
MOVQ AX, 16(SP)
|
||||
MOVQ CX, 24(SP)
|
||||
|
||||
// === Step 11: d += a1*2*a4 + 2*a2*a3 ===
|
||||
// Save a2 before doubling (needed later in step 16 and 19)
|
||||
MOVQ R10, 64(SP) // save original a2
|
||||
|
||||
MOVQ R9, DX
|
||||
MULXQ R15, AX, CX // a1 * 2*a4
|
||||
ADDQ AX, 0(SP)
|
||||
ADCQ CX, 8(SP)
|
||||
|
||||
MOVQ R10, DX
|
||||
ADDQ DX, DX // 2*a2
|
||||
MULXQ R11, AX, CX // 2*a2 * a3
|
||||
ADDQ AX, 0(SP)
|
||||
ADCQ CX, 8(SP)
|
||||
|
||||
// === Step 12: u0 = d & M; d >>= 52; u0 = (u0 << 4) | tx ===
|
||||
MOVQ 0(SP), AX
|
||||
ANDQ R14, AX
|
||||
SHLQ $4, AX
|
||||
ORQ 48(SP), AX
|
||||
MOVQ AX, 56(SP) // u0
|
||||
|
||||
MOVQ 0(SP), AX
|
||||
MOVQ 8(SP), CX
|
||||
SHRQ $52, AX
|
||||
MOVQ CX, DX
|
||||
SHLQ $12, DX
|
||||
ORQ DX, AX
|
||||
SHRQ $52, CX
|
||||
MOVQ AX, 0(SP)
|
||||
MOVQ CX, 8(SP)
|
||||
|
||||
// === Step 13: c += (R >> 4) * u0 ===
|
||||
MOVQ 56(SP), DX
|
||||
MOVQ $0x1000003D1, R13
|
||||
MULXQ R13, AX, CX
|
||||
ADDQ AX, 16(SP)
|
||||
ADCQ CX, 24(SP)
|
||||
|
||||
// === Step 14: r[0] = c & M; c >>= 52 ===
|
||||
MOVQ 16(SP), AX
|
||||
ANDQ R14, AX
|
||||
MOVQ AX, 0(DI)
|
||||
|
||||
MOVQ 16(SP), AX
|
||||
MOVQ 24(SP), CX
|
||||
SHRQ $52, AX
|
||||
MOVQ CX, DX
|
||||
SHLQ $12, DX
|
||||
ORQ DX, AX
|
||||
SHRQ $52, CX
|
||||
MOVQ AX, 16(SP)
|
||||
MOVQ CX, 24(SP)
|
||||
|
||||
// === Steps 15-16: Parallel c and d updates using ADCX/ADOX ===
|
||||
// Step 15: c += 2*a0*a1 (CF chain via ADCX)
|
||||
// Step 16: d += a2*2*a4 + a3*a3 (OF chain via ADOX)
|
||||
// Save r pointer and load accumulators
|
||||
MOVQ DI, 72(SP) // save r pointer (64(SP) has saved a2)
|
||||
|
||||
MOVQ 16(SP), R13 // c_lo
|
||||
MOVQ 24(SP), BX // c_hi (use BX since we need SI/DI)
|
||||
MOVQ 0(SP), SI // d_lo
|
||||
MOVQ 8(SP), DI // d_hi
|
||||
|
||||
// Clear CF and OF
|
||||
XORQ AX, AX
|
||||
|
||||
// c += 2*a0*a1
|
||||
MOVQ R8, DX
|
||||
ADDQ DX, DX // 2*a0
|
||||
MULXQ R9, AX, CX // 2*a0 * a1 -> CX:AX
|
||||
ADCXQ AX, R13 // c_lo += lo (CF chain)
|
||||
ADCXQ CX, BX // c_hi += hi + CF
|
||||
|
||||
// d += a2*2*a4
|
||||
MOVQ 64(SP), DX // load saved original a2
|
||||
MULXQ R15, AX, CX // a2 * 2*a4 -> CX:AX
|
||||
ADOXQ AX, SI // d_lo += lo (OF chain)
|
||||
ADOXQ CX, DI // d_hi += hi + OF
|
||||
|
||||
// d += a3*a3
|
||||
MOVQ R11, DX
|
||||
MULXQ R11, AX, CX // a3 * a3 -> CX:AX
|
||||
ADOXQ AX, SI // d_lo += lo
|
||||
ADOXQ CX, DI // d_hi += hi + OF
|
||||
|
||||
// Store results back
|
||||
MOVQ R13, 16(SP) // c_lo
|
||||
MOVQ BX, 24(SP) // c_hi
|
||||
MOVQ SI, 0(SP) // d_lo
|
||||
MOVQ DI, 8(SP) // d_hi
|
||||
MOVQ 72(SP), DI // restore r pointer
|
||||
|
||||
// === Step 17: c += R * (d & M); d >>= 52 ===
|
||||
MOVQ 0(SP), AX
|
||||
ANDQ R14, AX
|
||||
MOVQ AX, DX
|
||||
MOVQ $0x1000003D10, R13
|
||||
MULXQ R13, AX, CX
|
||||
ADDQ AX, 16(SP)
|
||||
ADCQ CX, 24(SP)
|
||||
|
||||
MOVQ 0(SP), AX
|
||||
MOVQ 8(SP), CX
|
||||
SHRQ $52, AX
|
||||
MOVQ CX, DX
|
||||
SHLQ $12, DX
|
||||
ORQ DX, AX
|
||||
SHRQ $52, CX
|
||||
MOVQ AX, 0(SP)
|
||||
MOVQ CX, 8(SP)
|
||||
|
||||
// === Step 18: r[1] = c & M; c >>= 52 ===
|
||||
MOVQ 16(SP), AX
|
||||
ANDQ R14, AX
|
||||
MOVQ AX, 8(DI)
|
||||
|
||||
MOVQ 16(SP), AX
|
||||
MOVQ 24(SP), CX
|
||||
SHRQ $52, AX
|
||||
MOVQ CX, DX
|
||||
SHLQ $12, DX
|
||||
ORQ DX, AX
|
||||
SHRQ $52, CX
|
||||
MOVQ AX, 16(SP)
|
||||
MOVQ CX, 24(SP)
|
||||
|
||||
// === Steps 19-20: Parallel c and d updates using ADCX/ADOX ===
|
||||
// Step 19: c += 2*a0*a2 + a1*a1 (CF chain via ADCX)
|
||||
// Step 20: d += a3*2*a4 (OF chain via ADOX)
|
||||
// Save r pointer and load accumulators
|
||||
MOVQ DI, 72(SP) // save r pointer
|
||||
|
||||
MOVQ 16(SP), R13 // c_lo
|
||||
MOVQ 24(SP), BX // c_hi
|
||||
MOVQ 0(SP), SI // d_lo
|
||||
MOVQ 8(SP), DI // d_hi
|
||||
|
||||
// Clear CF and OF
|
||||
XORQ AX, AX
|
||||
|
||||
// c += 2*a0*a2
|
||||
MOVQ R8, DX // a0 (R8 was never modified)
|
||||
ADDQ DX, DX // 2*a0
|
||||
MOVQ 64(SP), AX // load saved original a2
|
||||
MULXQ AX, AX, CX // 2*a0 * a2 -> CX:AX
|
||||
ADCXQ AX, R13 // c_lo += lo
|
||||
ADCXQ CX, BX // c_hi += hi + CF
|
||||
|
||||
// d += a3*2*a4
|
||||
MOVQ R11, DX
|
||||
MULXQ R15, AX, CX // a3 * 2*a4 -> CX:AX
|
||||
ADOXQ AX, SI // d_lo += lo
|
||||
ADOXQ CX, DI // d_hi += hi + OF
|
||||
|
||||
// c += a1*a1
|
||||
MOVQ R9, DX
|
||||
MULXQ R9, AX, CX // a1 * a1 -> CX:AX
|
||||
ADCXQ AX, R13 // c_lo += lo
|
||||
ADCXQ CX, BX // c_hi += hi + CF
|
||||
|
||||
// Store results back
|
||||
MOVQ R13, 16(SP) // c_lo
|
||||
MOVQ BX, 24(SP) // c_hi
|
||||
MOVQ SI, 0(SP) // d_lo
|
||||
MOVQ DI, 8(SP) // d_hi
|
||||
MOVQ 72(SP), DI // restore r pointer
|
||||
|
||||
// === Step 21: c += R * d_lo; d >>= 64 ===
|
||||
MOVQ 0(SP), DX
|
||||
MOVQ $0x1000003D10, R13
|
||||
MULXQ R13, AX, CX
|
||||
ADDQ AX, 16(SP)
|
||||
ADCQ CX, 24(SP)
|
||||
|
||||
MOVQ 8(SP), AX
|
||||
MOVQ AX, 0(SP)
|
||||
MOVQ $0, 8(SP)
|
||||
|
||||
// === Step 22: r[2] = c & M; c >>= 52 ===
|
||||
MOVQ 16(SP), AX
|
||||
ANDQ R14, AX
|
||||
MOVQ AX, 16(DI)
|
||||
|
||||
MOVQ 16(SP), AX
|
||||
MOVQ 24(SP), CX
|
||||
SHRQ $52, AX
|
||||
MOVQ CX, DX
|
||||
SHLQ $12, DX
|
||||
ORQ DX, AX
|
||||
SHRQ $52, CX
|
||||
MOVQ AX, 16(SP)
|
||||
MOVQ CX, 24(SP)
|
||||
|
||||
// === Step 23: c += (R << 12) * d + t3 ===
|
||||
MOVQ 0(SP), DX
|
||||
MOVQ $0x1000003D10000, R13
|
||||
MULXQ R13, AX, CX
|
||||
ADDQ AX, 16(SP)
|
||||
ADCQ CX, 24(SP)
|
||||
|
||||
MOVQ 32(SP), AX
|
||||
ADDQ AX, 16(SP)
|
||||
ADCQ $0, 24(SP)
|
||||
|
||||
// === Step 24: r[3] = c & M; c >>= 52 ===
|
||||
MOVQ 16(SP), AX
|
||||
ANDQ R14, AX
|
||||
MOVQ AX, 24(DI)
|
||||
|
||||
MOVQ 16(SP), AX
|
||||
MOVQ 24(SP), CX
|
||||
SHRQ $52, AX
|
||||
MOVQ CX, DX
|
||||
SHLQ $12, DX
|
||||
ORQ DX, AX
|
||||
|
||||
// === Step 25: r[4] = c + t4 ===
|
||||
ADDQ 40(SP), AX
|
||||
MOVQ AX, 32(DI)
|
||||
|
||||
RET
|
||||
@@ -196,3 +196,293 @@ func TestFieldSqrAsmVsPureGo(t *testing.T) {
|
||||
t.Skip("Assembly not available")
|
||||
}
|
||||
}
|
||||
|
||||
// BMI2 tests
|
||||
|
||||
func TestFieldMulAsmBMI2VsPureGo(t *testing.T) {
|
||||
if !hasFieldAsmBMI2() {
|
||||
t.Skip("BMI2+ADX assembly not available")
|
||||
}
|
||||
|
||||
// Test with simple values first
|
||||
a := FieldElement{n: [5]uint64{1, 0, 0, 0, 0}, magnitude: 1, normalized: true}
|
||||
b := FieldElement{n: [5]uint64{2, 0, 0, 0, 0}, magnitude: 1, normalized: true}
|
||||
|
||||
var rBMI2, rGo FieldElement
|
||||
|
||||
// Pure Go
|
||||
fieldMulPureGo(&rGo, &a, &b)
|
||||
|
||||
// BMI2 Assembly
|
||||
fieldMulAsmBMI2(&rBMI2, &a, &b)
|
||||
rBMI2.magnitude = 1
|
||||
rBMI2.normalized = false
|
||||
|
||||
t.Logf("a = %v", a.n)
|
||||
t.Logf("b = %v", b.n)
|
||||
t.Logf("Go result: %v", rGo.n)
|
||||
t.Logf("BMI2 result: %v", rBMI2.n)
|
||||
|
||||
for i := 0; i < 5; i++ {
|
||||
if rBMI2.n[i] != rGo.n[i] {
|
||||
t.Errorf("limb %d mismatch: bmi2=%x, go=%x", i, rBMI2.n[i], rGo.n[i])
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
func TestFieldMulAsmBMI2VsPureGoLarger(t *testing.T) {
|
||||
if !hasFieldAsmBMI2() {
|
||||
t.Skip("BMI2+ADX assembly not available")
|
||||
}
|
||||
|
||||
// Test with larger values
|
||||
a := FieldElement{
|
||||
n: [5]uint64{0x1234567890abcdef & 0xFFFFFFFFFFFFF, 0xfedcba9876543210 & 0xFFFFFFFFFFFFF, 0x0123456789abcdef & 0xFFFFFFFFFFFFF, 0xfedcba0987654321 & 0xFFFFFFFFFFFFF, 0x0123456789ab & 0x0FFFFFFFFFFFF},
|
||||
magnitude: 1,
|
||||
normalized: true,
|
||||
}
|
||||
b := FieldElement{
|
||||
n: [5]uint64{0xabcdef1234567890 & 0xFFFFFFFFFFFFF, 0x9876543210fedcba & 0xFFFFFFFFFFFFF, 0xfedcba1234567890 & 0xFFFFFFFFFFFFF, 0x0987654321abcdef & 0xFFFFFFFFFFFFF, 0x0fedcba98765 & 0x0FFFFFFFFFFFF},
|
||||
magnitude: 1,
|
||||
normalized: true,
|
||||
}
|
||||
|
||||
var rBMI2, rGo FieldElement
|
||||
|
||||
// Pure Go
|
||||
fieldMulPureGo(&rGo, &a, &b)
|
||||
|
||||
// BMI2 Assembly
|
||||
fieldMulAsmBMI2(&rBMI2, &a, &b)
|
||||
rBMI2.magnitude = 1
|
||||
rBMI2.normalized = false
|
||||
|
||||
t.Logf("a = %v", a.n)
|
||||
t.Logf("b = %v", b.n)
|
||||
t.Logf("Go result: %v", rGo.n)
|
||||
t.Logf("BMI2 result: %v", rBMI2.n)
|
||||
|
||||
for i := 0; i < 5; i++ {
|
||||
if rBMI2.n[i] != rGo.n[i] {
|
||||
t.Errorf("limb %d mismatch: bmi2=%x, go=%x", i, rBMI2.n[i], rGo.n[i])
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
func TestFieldMulAsmBMI2VsRegularAsm(t *testing.T) {
|
||||
if !hasFieldAsmBMI2() {
|
||||
t.Skip("BMI2+ADX assembly not available")
|
||||
}
|
||||
if !hasFieldAsm() {
|
||||
t.Skip("Regular assembly not available")
|
||||
}
|
||||
|
||||
// Test with larger values
|
||||
a := FieldElement{
|
||||
n: [5]uint64{0x1234567890abcdef & 0xFFFFFFFFFFFFF, 0xfedcba9876543210 & 0xFFFFFFFFFFFFF, 0x0123456789abcdef & 0xFFFFFFFFFFFFF, 0xfedcba0987654321 & 0xFFFFFFFFFFFFF, 0x0123456789ab & 0x0FFFFFFFFFFFF},
|
||||
magnitude: 1,
|
||||
normalized: true,
|
||||
}
|
||||
b := FieldElement{
|
||||
n: [5]uint64{0xabcdef1234567890 & 0xFFFFFFFFFFFFF, 0x9876543210fedcba & 0xFFFFFFFFFFFFF, 0xfedcba1234567890 & 0xFFFFFFFFFFFFF, 0x0987654321abcdef & 0xFFFFFFFFFFFFF, 0x0fedcba98765 & 0x0FFFFFFFFFFFF},
|
||||
magnitude: 1,
|
||||
normalized: true,
|
||||
}
|
||||
|
||||
var rBMI2, rAsm FieldElement
|
||||
|
||||
// Regular Assembly
|
||||
fieldMulAsm(&rAsm, &a, &b)
|
||||
rAsm.magnitude = 1
|
||||
rAsm.normalized = false
|
||||
|
||||
// BMI2 Assembly
|
||||
fieldMulAsmBMI2(&rBMI2, &a, &b)
|
||||
rBMI2.magnitude = 1
|
||||
rBMI2.normalized = false
|
||||
|
||||
t.Logf("a = %v", a.n)
|
||||
t.Logf("b = %v", b.n)
|
||||
t.Logf("Asm result: %v", rAsm.n)
|
||||
t.Logf("BMI2 result: %v", rBMI2.n)
|
||||
|
||||
for i := 0; i < 5; i++ {
|
||||
if rBMI2.n[i] != rAsm.n[i] {
|
||||
t.Errorf("limb %d mismatch: bmi2=%x, asm=%x", i, rBMI2.n[i], rAsm.n[i])
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
func TestFieldSqrAsmBMI2VsPureGo(t *testing.T) {
|
||||
if !hasFieldAsmBMI2() {
|
||||
t.Skip("BMI2+ADX assembly not available")
|
||||
}
|
||||
|
||||
a := FieldElement{
|
||||
n: [5]uint64{0x1234567890abcdef & 0xFFFFFFFFFFFFF, 0xfedcba9876543210 & 0xFFFFFFFFFFFFF, 0x0123456789abcdef & 0xFFFFFFFFFFFFF, 0xfedcba0987654321 & 0xFFFFFFFFFFFFF, 0x0123456789ab & 0x0FFFFFFFFFFFF},
|
||||
magnitude: 1,
|
||||
normalized: true,
|
||||
}
|
||||
|
||||
var rBMI2, rGo FieldElement
|
||||
|
||||
// Pure Go (a * a)
|
||||
fieldMulPureGo(&rGo, &a, &a)
|
||||
|
||||
// BMI2 Assembly
|
||||
fieldSqrAsmBMI2(&rBMI2, &a)
|
||||
rBMI2.magnitude = 1
|
||||
rBMI2.normalized = false
|
||||
|
||||
t.Logf("a = %v", a.n)
|
||||
t.Logf("Go result: %v", rGo.n)
|
||||
t.Logf("BMI2 result: %v", rBMI2.n)
|
||||
|
||||
for i := 0; i < 5; i++ {
|
||||
if rBMI2.n[i] != rGo.n[i] {
|
||||
t.Errorf("limb %d mismatch: bmi2=%x, go=%x", i, rBMI2.n[i], rGo.n[i])
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
func TestFieldSqrAsmBMI2VsRegularAsm(t *testing.T) {
|
||||
if !hasFieldAsmBMI2() {
|
||||
t.Skip("BMI2+ADX assembly not available")
|
||||
}
|
||||
if !hasFieldAsm() {
|
||||
t.Skip("Regular assembly not available")
|
||||
}
|
||||
|
||||
a := FieldElement{
|
||||
n: [5]uint64{0x1234567890abcdef & 0xFFFFFFFFFFFFF, 0xfedcba9876543210 & 0xFFFFFFFFFFFFF, 0x0123456789abcdef & 0xFFFFFFFFFFFFF, 0xfedcba0987654321 & 0xFFFFFFFFFFFFF, 0x0123456789ab & 0x0FFFFFFFFFFFF},
|
||||
magnitude: 1,
|
||||
normalized: true,
|
||||
}
|
||||
|
||||
var rBMI2, rAsm FieldElement
|
||||
|
||||
// Regular Assembly
|
||||
fieldSqrAsm(&rAsm, &a)
|
||||
rAsm.magnitude = 1
|
||||
rAsm.normalized = false
|
||||
|
||||
// BMI2 Assembly
|
||||
fieldSqrAsmBMI2(&rBMI2, &a)
|
||||
rBMI2.magnitude = 1
|
||||
rBMI2.normalized = false
|
||||
|
||||
t.Logf("a = %v", a.n)
|
||||
t.Logf("Asm result: %v", rAsm.n)
|
||||
t.Logf("BMI2 result: %v", rBMI2.n)
|
||||
|
||||
for i := 0; i < 5; i++ {
|
||||
if rBMI2.n[i] != rAsm.n[i] {
|
||||
t.Errorf("limb %d mismatch: bmi2=%x, asm=%x", i, rBMI2.n[i], rAsm.n[i])
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// TestFieldMulAsmBMI2Random tests with many random values
|
||||
func TestFieldMulAsmBMI2Random(t *testing.T) {
|
||||
if !hasFieldAsmBMI2() {
|
||||
t.Skip("BMI2+ADX assembly not available")
|
||||
}
|
||||
if !hasFieldAsm() {
|
||||
t.Skip("Regular assembly not available")
|
||||
}
|
||||
|
||||
// Test with many random values
|
||||
for iter := 0; iter < 10000; iter++ {
|
||||
var a, b FieldElement
|
||||
a.magnitude = 1
|
||||
a.normalized = true
|
||||
b.magnitude = 1
|
||||
b.normalized = true
|
||||
|
||||
// Generate deterministic but varied test data
|
||||
seed := uint64(iter * 12345678901234567)
|
||||
for j := 0; j < 5; j++ {
|
||||
seed = seed*6364136223846793005 + 1442695040888963407 // LCG
|
||||
a.n[j] = seed & 0xFFFFFFFFFFFFF
|
||||
|
||||
seed = seed*6364136223846793005 + 1442695040888963407
|
||||
b.n[j] = seed & 0xFFFFFFFFFFFFF
|
||||
}
|
||||
// Limb 4 is only 48 bits
|
||||
a.n[4] &= 0x0FFFFFFFFFFFF
|
||||
b.n[4] &= 0x0FFFFFFFFFFFF
|
||||
|
||||
var rAsm, rBMI2 FieldElement
|
||||
|
||||
// Regular Assembly
|
||||
fieldMulAsm(&rAsm, &a, &b)
|
||||
rAsm.magnitude = 1
|
||||
rAsm.normalized = false
|
||||
|
||||
// BMI2 Assembly
|
||||
fieldMulAsmBMI2(&rBMI2, &a, &b)
|
||||
rBMI2.magnitude = 1
|
||||
rBMI2.normalized = false
|
||||
|
||||
// Compare results
|
||||
for j := 0; j < 5; j++ {
|
||||
if rAsm.n[j] != rBMI2.n[j] {
|
||||
t.Errorf("Iteration %d: limb %d mismatch", iter, j)
|
||||
t.Errorf(" a = %v", a.n)
|
||||
t.Errorf(" b = %v", b.n)
|
||||
t.Errorf(" Asm: %v", rAsm.n)
|
||||
t.Errorf(" BMI2: %v", rBMI2.n)
|
||||
return
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// TestFieldSqrAsmBMI2Random tests squaring with many random values
|
||||
func TestFieldSqrAsmBMI2Random(t *testing.T) {
|
||||
if !hasFieldAsmBMI2() {
|
||||
t.Skip("BMI2+ADX assembly not available")
|
||||
}
|
||||
if !hasFieldAsm() {
|
||||
t.Skip("Regular assembly not available")
|
||||
}
|
||||
|
||||
// Test with many random values
|
||||
for iter := 0; iter < 10000; iter++ {
|
||||
var a FieldElement
|
||||
a.magnitude = 1
|
||||
a.normalized = true
|
||||
|
||||
// Generate deterministic but varied test data
|
||||
seed := uint64(iter * 98765432109876543)
|
||||
for j := 0; j < 5; j++ {
|
||||
seed = seed*6364136223846793005 + 1442695040888963407 // LCG
|
||||
a.n[j] = seed & 0xFFFFFFFFFFFFF
|
||||
}
|
||||
// Limb 4 is only 48 bits
|
||||
a.n[4] &= 0x0FFFFFFFFFFFF
|
||||
|
||||
var rAsm, rBMI2 FieldElement
|
||||
|
||||
// Regular Assembly
|
||||
fieldSqrAsm(&rAsm, &a)
|
||||
rAsm.magnitude = 1
|
||||
rAsm.normalized = false
|
||||
|
||||
// BMI2 Assembly
|
||||
fieldSqrAsmBMI2(&rBMI2, &a)
|
||||
rBMI2.magnitude = 1
|
||||
rBMI2.normalized = false
|
||||
|
||||
// Compare results
|
||||
for j := 0; j < 5; j++ {
|
||||
if rAsm.n[j] != rBMI2.n[j] {
|
||||
t.Errorf("Iteration %d: limb %d mismatch", iter, j)
|
||||
t.Errorf(" a = %v", a.n)
|
||||
t.Errorf(" Asm: %v", rAsm.n)
|
||||
t.Errorf(" BMI2: %v", rBMI2.n)
|
||||
return
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
@@ -74,3 +74,29 @@ func BenchmarkFieldSqr(b *testing.B) {
|
||||
r.sqr(&a)
|
||||
}
|
||||
}
|
||||
|
||||
// BMI2 benchmarks
|
||||
|
||||
// BenchmarkFieldMulAsmBMI2 benchmarks the BMI2 assembly field multiplication
|
||||
func BenchmarkFieldMulAsmBMI2(b *testing.B) {
|
||||
if !hasFieldAsmBMI2() {
|
||||
b.Skip("BMI2+ADX assembly not available")
|
||||
}
|
||||
|
||||
var r FieldElement
|
||||
for i := 0; i < b.N; i++ {
|
||||
fieldMulAsmBMI2(&r, &benchFieldA, &benchFieldB)
|
||||
}
|
||||
}
|
||||
|
||||
// BenchmarkFieldSqrAsmBMI2 benchmarks the BMI2 assembly field squaring
|
||||
func BenchmarkFieldSqrAsmBMI2(b *testing.B) {
|
||||
if !hasFieldAsmBMI2() {
|
||||
b.Skip("BMI2+ADX assembly not available")
|
||||
}
|
||||
|
||||
var r FieldElement
|
||||
for i := 0; i < b.N; i++ {
|
||||
fieldSqrAsmBMI2(&r, &benchFieldA)
|
||||
}
|
||||
}
|
||||
|
||||
@@ -8,6 +8,12 @@ func hasFieldAsm() bool {
|
||||
return false
|
||||
}
|
||||
|
||||
// hasFieldAsmBMI2 returns true if BMI2+ADX optimized field assembly is available.
|
||||
// On non-amd64 platforms, this is always false.
|
||||
func hasFieldAsmBMI2() bool {
|
||||
return false
|
||||
}
|
||||
|
||||
// fieldMulAsm is a stub for non-amd64 platforms.
|
||||
// It should never be called since hasFieldAsm() returns false.
|
||||
func fieldMulAsm(r, a, b *FieldElement) {
|
||||
@@ -19,3 +25,15 @@ func fieldMulAsm(r, a, b *FieldElement) {
|
||||
func fieldSqrAsm(r, a *FieldElement) {
|
||||
panic("field assembly not available on this platform")
|
||||
}
|
||||
|
||||
// fieldMulAsmBMI2 is a stub for non-amd64 platforms.
|
||||
// It should never be called since hasFieldAsmBMI2() returns false.
|
||||
func fieldMulAsmBMI2(r, a, b *FieldElement) {
|
||||
panic("field BMI2 assembly not available on this platform")
|
||||
}
|
||||
|
||||
// fieldSqrAsmBMI2 is a stub for non-amd64 platforms.
|
||||
// It should never be called since hasFieldAsmBMI2() returns false.
|
||||
func fieldSqrAsmBMI2(r, a *FieldElement) {
|
||||
panic("field BMI2 assembly not available on this platform")
|
||||
}
|
||||
|
||||
20
field_mul.go
20
field_mul.go
@@ -78,7 +78,15 @@ func (r *FieldElement) mul(a, b *FieldElement) {
|
||||
bNorm = b // Use directly, no copy needed
|
||||
}
|
||||
|
||||
// Use assembly if available
|
||||
// Use BMI2+ADX assembly if available (fastest)
|
||||
if hasFieldAsmBMI2() {
|
||||
fieldMulAsmBMI2(r, aNorm, bNorm)
|
||||
r.magnitude = 1
|
||||
r.normalized = false
|
||||
return
|
||||
}
|
||||
|
||||
// Use regular assembly if available
|
||||
if hasFieldAsm() {
|
||||
fieldMulAsm(r, aNorm, bNorm)
|
||||
r.magnitude = 1
|
||||
@@ -315,7 +323,15 @@ func (r *FieldElement) sqr(a *FieldElement) {
|
||||
aNorm = a // Use directly, no copy needed
|
||||
}
|
||||
|
||||
// Use assembly if available
|
||||
// Use BMI2+ADX assembly if available (fastest)
|
||||
if hasFieldAsmBMI2() {
|
||||
fieldSqrAsmBMI2(r, aNorm)
|
||||
r.magnitude = 1
|
||||
r.normalized = false
|
||||
return
|
||||
}
|
||||
|
||||
// Use regular assembly if available
|
||||
if hasFieldAsm() {
|
||||
fieldSqrAsm(r, aNorm)
|
||||
r.magnitude = 1
|
||||
|
||||
1958
glv_test.go
Normal file
1958
glv_test.go
Normal file
File diff suppressed because it is too large
Load Diff
8
go.mod
8
go.mod
@@ -3,12 +3,16 @@ module p256k1.mleku.dev
|
||||
go 1.25.0
|
||||
|
||||
require (
|
||||
github.com/btcsuite/btcd/btcec/v2 v2.3.6
|
||||
github.com/ebitengine/purego v0.9.1
|
||||
github.com/klauspost/cpuid/v2 v2.3.0
|
||||
github.com/minio/sha256-simd v1.0.1
|
||||
next.orly.dev v1.0.3
|
||||
)
|
||||
|
||||
require (
|
||||
github.com/ebitengine/purego v0.9.1 // indirect
|
||||
github.com/klauspost/cpuid/v2 v2.3.0 // indirect
|
||||
github.com/btcsuite/btcd/chaincfg/chainhash v1.0.1 // indirect
|
||||
github.com/decred/dcrd/crypto/blake256 v1.0.0 // indirect
|
||||
github.com/decred/dcrd/dcrec/secp256k1/v4 v4.0.1 // indirect
|
||||
golang.org/x/sys v0.37.0 // indirect
|
||||
)
|
||||
|
||||
10
go.sum
10
go.sum
@@ -1,3 +1,13 @@
|
||||
github.com/btcsuite/btcd/btcec/v2 v2.3.6 h1:IzlsEr9olcSRKB/n7c4351F3xHKxS2lma+1UFGCYd4E=
|
||||
github.com/btcsuite/btcd/btcec/v2 v2.3.6/go.mod h1:m22FrOAiuxl/tht9wIqAoGHcbnCCaPWyauO8y2LGGtQ=
|
||||
github.com/btcsuite/btcd/chaincfg/chainhash v1.0.1 h1:q0rUy8C/TYNBQS1+CGKw68tLOFYSNEs0TFnxxnS9+4U=
|
||||
github.com/btcsuite/btcd/chaincfg/chainhash v1.0.1/go.mod h1:7SFka0XMvUgj3hfZtydOrQY2mwhPclbT2snogU7SQQc=
|
||||
github.com/davecgh/go-spew v1.1.1 h1:vj9j/u1bqnvCEfJOwUhtlOARqs3+rkHYY13jYWTU97c=
|
||||
github.com/davecgh/go-spew v1.1.1/go.mod h1:J7Y8YcW2NihsgmVo/mv3lAwl/skON4iLHjSsI+c5H38=
|
||||
github.com/decred/dcrd/crypto/blake256 v1.0.0 h1:/8DMNYp9SGi5f0w7uCm6d6M4OU2rGFK09Y2A4Xv7EE0=
|
||||
github.com/decred/dcrd/crypto/blake256 v1.0.0/go.mod h1:sQl2p6Y26YV+ZOcSTP6thNdn47hh8kt6rqSlvmrXFAc=
|
||||
github.com/decred/dcrd/dcrec/secp256k1/v4 v4.0.1 h1:YLtO71vCjJRCBcrPMtQ9nqBsqpA1m5sE92cU+pd5Mcc=
|
||||
github.com/decred/dcrd/dcrec/secp256k1/v4 v4.0.1/go.mod h1:hyedUtir6IdtD/7lIxGeCxkaw7y45JueMRL4DIyJDKs=
|
||||
github.com/ebitengine/purego v0.9.1 h1:a/k2f2HQU3Pi399RPW1MOaZyhKJL9w/xFpKAg4q1s0A=
|
||||
github.com/ebitengine/purego v0.9.1/go.mod h1:iIjxzd6CiRiOG0UyXP+V1+jWqUXVjPKLAI0mRfJZTmQ=
|
||||
github.com/klauspost/cpuid/v2 v2.3.0 h1:S4CRMLnYUhGeDFDqkGriYKdfoFlDnMtqTiI/sFzhA9Y=
|
||||
|
||||
244
group.go
244
group.go
@@ -157,12 +157,30 @@ func (r *GroupElementAffine) negate(a *GroupElementAffine) {
|
||||
r.setInfinity()
|
||||
return
|
||||
}
|
||||
|
||||
|
||||
r.x = a.x
|
||||
r.y.negate(&a.y, a.y.magnitude)
|
||||
r.infinity = false
|
||||
}
|
||||
|
||||
// mulLambda applies the GLV endomorphism: λ·(x, y) = (β·x, y)
|
||||
// This is the key operation that enables the GLV optimization.
|
||||
// Since λ is a cube root of unity mod n, and β is a cube root of unity mod p,
|
||||
// multiplying a point by λ (scalar) is equivalent to multiplying x by β (field).
|
||||
// Reference: libsecp256k1 group_impl.h:secp256k1_ge_mul_lambda
|
||||
func (r *GroupElementAffine) mulLambda(a *GroupElementAffine) {
|
||||
if a.infinity {
|
||||
r.setInfinity()
|
||||
return
|
||||
}
|
||||
|
||||
// r.x = β * a.x
|
||||
r.x.mul(&a.x, &fieldBeta)
|
||||
// r.y = a.y (unchanged)
|
||||
r.y = a.y
|
||||
r.infinity = false
|
||||
}
|
||||
|
||||
// setInfinity sets the group element to the point at infinity
|
||||
func (r *GroupElementAffine) setInfinity() {
|
||||
r.x = FieldElementZero
|
||||
@@ -267,13 +285,29 @@ func (r *GroupElementJacobian) negate(a *GroupElementJacobian) {
|
||||
r.setInfinity()
|
||||
return
|
||||
}
|
||||
|
||||
|
||||
r.x = a.x
|
||||
r.y.negate(&a.y, a.y.magnitude)
|
||||
r.z = a.z
|
||||
r.infinity = false
|
||||
}
|
||||
|
||||
// mulLambda applies the GLV endomorphism to a Jacobian point: λ·(X, Y, Z) = (β·X, Y, Z)
|
||||
// In Jacobian coordinates, only the X coordinate is multiplied by β.
|
||||
func (r *GroupElementJacobian) mulLambda(a *GroupElementJacobian) {
|
||||
if a.infinity {
|
||||
r.setInfinity()
|
||||
return
|
||||
}
|
||||
|
||||
// r.x = β * a.x
|
||||
r.x.mul(&a.x, &fieldBeta)
|
||||
// r.y and r.z unchanged
|
||||
r.y = a.y
|
||||
r.z = a.z
|
||||
r.infinity = false
|
||||
}
|
||||
|
||||
// double sets r = 2*a (point doubling in Jacobian coordinates)
|
||||
// This follows the C secp256k1_gej_double implementation exactly
|
||||
func (r *GroupElementJacobian) double(a *GroupElementJacobian) {
|
||||
@@ -707,3 +741,209 @@ func (r *GroupElementAffine) fromBytes(buf []byte) {
|
||||
r.y.setB32(buf[32:64])
|
||||
r.infinity = false
|
||||
}
|
||||
|
||||
// BatchNormalize converts multiple Jacobian points to affine coordinates efficiently
|
||||
// using Montgomery's batch inversion trick. This computes n inversions using only
|
||||
// 1 actual inversion + 3(n-1) multiplications, which is much faster than n individual
|
||||
// inversions when n > 1.
|
||||
//
|
||||
// The input slice 'points' contains the Jacobian points to convert.
|
||||
// The output slice 'out' will contain the corresponding affine points.
|
||||
// If out is nil or smaller than points, a new slice will be allocated.
|
||||
//
|
||||
// Points at infinity are handled correctly and result in affine infinity points.
|
||||
func BatchNormalize(out []GroupElementAffine, points []GroupElementJacobian) []GroupElementAffine {
|
||||
n := len(points)
|
||||
if n == 0 {
|
||||
return out
|
||||
}
|
||||
|
||||
// Ensure output slice is large enough
|
||||
if out == nil || len(out) < n {
|
||||
out = make([]GroupElementAffine, n)
|
||||
}
|
||||
|
||||
// Handle single point case - no batch optimization needed
|
||||
if n == 1 {
|
||||
out[0].setGEJ(&points[0])
|
||||
return out
|
||||
}
|
||||
|
||||
// Collect non-infinity Z coordinates for batch inversion
|
||||
// We need to track which points are at infinity
|
||||
zValues := make([]FieldElement, 0, n)
|
||||
nonInfIndices := make([]int, 0, n)
|
||||
|
||||
for i := 0; i < n; i++ {
|
||||
if points[i].isInfinity() {
|
||||
out[i].setInfinity()
|
||||
} else {
|
||||
zValues = append(zValues, points[i].z)
|
||||
nonInfIndices = append(nonInfIndices, i)
|
||||
}
|
||||
}
|
||||
|
||||
// If all points are at infinity, we're done
|
||||
if len(zValues) == 0 {
|
||||
return out
|
||||
}
|
||||
|
||||
// Batch invert all Z values
|
||||
zInvs := make([]FieldElement, len(zValues))
|
||||
batchInverse(zInvs, zValues)
|
||||
|
||||
// Now compute affine coordinates for each non-infinity point
|
||||
// affine.x = X * Z^(-2)
|
||||
// affine.y = Y * Z^(-3)
|
||||
for i, idx := range nonInfIndices {
|
||||
var zInv2, zInv3 FieldElement
|
||||
|
||||
// zInv2 = Z^(-2)
|
||||
zInv2.sqr(&zInvs[i])
|
||||
|
||||
// zInv3 = Z^(-3) = Z^(-2) * Z^(-1)
|
||||
zInv3.mul(&zInv2, &zInvs[i])
|
||||
|
||||
// x = X * Z^(-2)
|
||||
out[idx].x.mul(&points[idx].x, &zInv2)
|
||||
|
||||
// y = Y * Z^(-3)
|
||||
out[idx].y.mul(&points[idx].y, &zInv3)
|
||||
|
||||
out[idx].infinity = false
|
||||
}
|
||||
|
||||
return out
|
||||
}
|
||||
|
||||
// BatchNormalizeInPlace converts multiple Jacobian points to affine coordinates
|
||||
// in place, modifying the input slice. Each Jacobian point is converted such that
|
||||
// Z becomes 1 (or the point is marked as infinity).
|
||||
//
|
||||
// This is useful when you want to normalize points without allocating new memory
|
||||
// for a separate affine point array.
|
||||
func BatchNormalizeInPlace(points []GroupElementJacobian) {
|
||||
n := len(points)
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
|
||||
// Handle single point case
|
||||
if n == 1 {
|
||||
if !points[0].isInfinity() {
|
||||
var zInv, zInv2, zInv3 FieldElement
|
||||
zInv.inv(&points[0].z)
|
||||
zInv2.sqr(&zInv)
|
||||
zInv3.mul(&zInv2, &zInv)
|
||||
points[0].x.mul(&points[0].x, &zInv2)
|
||||
points[0].y.mul(&points[0].y, &zInv3)
|
||||
points[0].z.setInt(1)
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
// Collect non-infinity Z coordinates for batch inversion
|
||||
zValues := make([]FieldElement, 0, n)
|
||||
nonInfIndices := make([]int, 0, n)
|
||||
|
||||
for i := 0; i < n; i++ {
|
||||
if !points[i].isInfinity() {
|
||||
zValues = append(zValues, points[i].z)
|
||||
nonInfIndices = append(nonInfIndices, i)
|
||||
}
|
||||
}
|
||||
|
||||
// If all points are at infinity, we're done
|
||||
if len(zValues) == 0 {
|
||||
return
|
||||
}
|
||||
|
||||
// Batch invert all Z values
|
||||
zInvs := make([]FieldElement, len(zValues))
|
||||
batchInverse(zInvs, zValues)
|
||||
|
||||
// Now normalize each non-infinity point
|
||||
for i, idx := range nonInfIndices {
|
||||
var zInv2, zInv3 FieldElement
|
||||
|
||||
// zInv2 = Z^(-2)
|
||||
zInv2.sqr(&zInvs[i])
|
||||
|
||||
// zInv3 = Z^(-3) = Z^(-2) * Z^(-1)
|
||||
zInv3.mul(&zInv2, &zInvs[i])
|
||||
|
||||
// x = X * Z^(-2)
|
||||
points[idx].x.mul(&points[idx].x, &zInv2)
|
||||
|
||||
// y = Y * Z^(-3)
|
||||
points[idx].y.mul(&points[idx].y, &zInv3)
|
||||
|
||||
// Z = 1
|
||||
points[idx].z.setInt(1)
|
||||
}
|
||||
}
|
||||
|
||||
// =============================================================================
|
||||
// GLV Endomorphism Support Functions
|
||||
// =============================================================================
|
||||
|
||||
// ecmultEndoSplit splits a scalar and point for the GLV endomorphism optimization.
|
||||
// Given a scalar s and point p, it computes:
|
||||
// s1, s2 such that s1 + s2*λ ≡ s (mod n)
|
||||
// p1 = p
|
||||
// p2 = λ*p = (β*p.x, p.y)
|
||||
//
|
||||
// It also normalizes s1 and s2 to be "low" (not high) by conditionally negating
|
||||
// both the scalar and corresponding point.
|
||||
//
|
||||
// After this function:
|
||||
// s1 * p1 + s2 * p2 = s * p
|
||||
//
|
||||
// Reference: libsecp256k1 ecmult_impl.h:secp256k1_ecmult_endo_split
|
||||
func ecmultEndoSplit(s1, s2 *Scalar, p1, p2 *GroupElementAffine, s *Scalar, p *GroupElementAffine) {
|
||||
// Split the scalar: s = s1 + s2*λ
|
||||
scalarSplitLambda(s1, s2, s)
|
||||
|
||||
// p1 = p (copy)
|
||||
*p1 = *p
|
||||
|
||||
// p2 = λ*p = (β*p.x, p.y)
|
||||
p2.mulLambda(p)
|
||||
|
||||
// If s1 is high, negate it and p1
|
||||
if s1.isHigh() {
|
||||
s1.negate(s1)
|
||||
p1.negate(p1)
|
||||
}
|
||||
|
||||
// If s2 is high, negate it and p2
|
||||
if s2.isHigh() {
|
||||
s2.negate(s2)
|
||||
p2.negate(p2)
|
||||
}
|
||||
}
|
||||
|
||||
// ecmultEndoSplitJac is the Jacobian version of ecmultEndoSplit.
|
||||
// Given a scalar s and Jacobian point p, it computes the split for GLV optimization.
|
||||
func ecmultEndoSplitJac(s1, s2 *Scalar, p1, p2 *GroupElementJacobian, s *Scalar, p *GroupElementJacobian) {
|
||||
// Split the scalar: s = s1 + s2*λ
|
||||
scalarSplitLambda(s1, s2, s)
|
||||
|
||||
// p1 = p (copy)
|
||||
*p1 = *p
|
||||
|
||||
// p2 = λ*p = (β*p.x, p.y, p.z)
|
||||
p2.mulLambda(p)
|
||||
|
||||
// If s1 is high, negate it and p1
|
||||
if s1.isHigh() {
|
||||
s1.negate(s1)
|
||||
p1.negate(p1)
|
||||
}
|
||||
|
||||
// If s2 is high, negate it and p2
|
||||
if s2.isHigh() {
|
||||
s2.negate(s2)
|
||||
p2.negate(p2)
|
||||
}
|
||||
}
|
||||
|
||||
177
group_test.go
177
group_test.go
@@ -1,6 +1,7 @@
|
||||
package p256k1
|
||||
|
||||
import (
|
||||
"fmt"
|
||||
"testing"
|
||||
)
|
||||
|
||||
@@ -139,3 +140,179 @@ func BenchmarkGroupAdd(b *testing.B) {
|
||||
jac1.addVar(&jac1, &jac2)
|
||||
}
|
||||
}
|
||||
|
||||
// TestBatchNormalize tests that BatchNormalize produces the same results as individual conversions
|
||||
func TestBatchNormalize(t *testing.T) {
|
||||
// Create several Jacobian points: G, 2G, 3G, 4G, ...
|
||||
n := 10
|
||||
points := make([]GroupElementJacobian, n)
|
||||
expected := make([]GroupElementAffine, n)
|
||||
|
||||
var current GroupElementJacobian
|
||||
current.setGE(&Generator)
|
||||
|
||||
for i := 0; i < n; i++ {
|
||||
points[i] = current
|
||||
// Get expected result using individual conversion
|
||||
expected[i].setGEJ(¤t)
|
||||
// Move to next point
|
||||
var next GroupElementJacobian
|
||||
next.addVar(¤t, &points[0]) // Add G each time
|
||||
current = next
|
||||
}
|
||||
|
||||
// Now use BatchNormalize
|
||||
result := BatchNormalize(nil, points)
|
||||
|
||||
// Compare results
|
||||
for i := 0; i < n; i++ {
|
||||
// Normalize both for comparison
|
||||
expected[i].x.normalize()
|
||||
expected[i].y.normalize()
|
||||
result[i].x.normalize()
|
||||
result[i].y.normalize()
|
||||
|
||||
if !expected[i].x.equal(&result[i].x) {
|
||||
t.Errorf("Point %d: X mismatch", i)
|
||||
}
|
||||
if !expected[i].y.equal(&result[i].y) {
|
||||
t.Errorf("Point %d: Y mismatch", i)
|
||||
}
|
||||
if expected[i].infinity != result[i].infinity {
|
||||
t.Errorf("Point %d: infinity mismatch", i)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// TestBatchNormalizeWithInfinity tests that BatchNormalize handles infinity points correctly
|
||||
func TestBatchNormalizeWithInfinity(t *testing.T) {
|
||||
points := make([]GroupElementJacobian, 5)
|
||||
|
||||
// Set some points to generator, some to infinity
|
||||
points[0].setGE(&Generator)
|
||||
points[1].setInfinity()
|
||||
points[2].setGE(&Generator)
|
||||
points[2].double(&points[2]) // 2G
|
||||
points[3].setInfinity()
|
||||
points[4].setGE(&Generator)
|
||||
|
||||
result := BatchNormalize(nil, points)
|
||||
|
||||
// Check infinity points
|
||||
if !result[1].isInfinity() {
|
||||
t.Error("Point 1 should be infinity")
|
||||
}
|
||||
if !result[3].isInfinity() {
|
||||
t.Error("Point 3 should be infinity")
|
||||
}
|
||||
|
||||
// Check non-infinity points
|
||||
if result[0].isInfinity() {
|
||||
t.Error("Point 0 should not be infinity")
|
||||
}
|
||||
if result[2].isInfinity() {
|
||||
t.Error("Point 2 should not be infinity")
|
||||
}
|
||||
if result[4].isInfinity() {
|
||||
t.Error("Point 4 should not be infinity")
|
||||
}
|
||||
|
||||
// Verify non-infinity points are on the curve
|
||||
if !result[0].isValid() {
|
||||
t.Error("Point 0 should be valid")
|
||||
}
|
||||
if !result[2].isValid() {
|
||||
t.Error("Point 2 should be valid")
|
||||
}
|
||||
if !result[4].isValid() {
|
||||
t.Error("Point 4 should be valid")
|
||||
}
|
||||
}
|
||||
|
||||
// TestBatchNormalizeInPlace tests in-place batch normalization
|
||||
func TestBatchNormalizeInPlace(t *testing.T) {
|
||||
n := 5
|
||||
points := make([]GroupElementJacobian, n)
|
||||
expected := make([]GroupElementAffine, n)
|
||||
|
||||
var current GroupElementJacobian
|
||||
current.setGE(&Generator)
|
||||
|
||||
for i := 0; i < n; i++ {
|
||||
points[i] = current
|
||||
expected[i].setGEJ(¤t)
|
||||
var next GroupElementJacobian
|
||||
next.addVar(¤t, &points[0])
|
||||
current = next
|
||||
}
|
||||
|
||||
// Normalize in place
|
||||
BatchNormalizeInPlace(points)
|
||||
|
||||
// After normalization, Z should be 1 for all non-infinity points
|
||||
for i := 0; i < n; i++ {
|
||||
if !points[i].isInfinity() {
|
||||
var one FieldElement
|
||||
one.setInt(1)
|
||||
points[i].z.normalize()
|
||||
if !points[i].z.equal(&one) {
|
||||
t.Errorf("Point %d: Z should be 1 after normalization", i)
|
||||
}
|
||||
}
|
||||
|
||||
// Check X and Y match expected
|
||||
points[i].x.normalize()
|
||||
points[i].y.normalize()
|
||||
expected[i].x.normalize()
|
||||
expected[i].y.normalize()
|
||||
|
||||
if !points[i].x.equal(&expected[i].x) {
|
||||
t.Errorf("Point %d: X mismatch after in-place normalization", i)
|
||||
}
|
||||
if !points[i].y.equal(&expected[i].y) {
|
||||
t.Errorf("Point %d: Y mismatch after in-place normalization", i)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// BenchmarkBatchNormalize benchmarks batch normalization vs individual conversions
|
||||
func BenchmarkBatchNormalize(b *testing.B) {
|
||||
sizes := []int{1, 2, 4, 8, 16, 32, 64}
|
||||
|
||||
for _, size := range sizes {
|
||||
n := size // capture for closure
|
||||
|
||||
// Create n Jacobian points
|
||||
points := make([]GroupElementJacobian, n)
|
||||
var current GroupElementJacobian
|
||||
current.setGE(&Generator)
|
||||
for i := 0; i < n; i++ {
|
||||
points[i] = current
|
||||
current.double(¤t)
|
||||
}
|
||||
|
||||
b.Run(
|
||||
fmt.Sprintf("Individual_%d", n),
|
||||
func(b *testing.B) {
|
||||
out := make([]GroupElementAffine, n)
|
||||
b.ResetTimer()
|
||||
for i := 0; i < b.N; i++ {
|
||||
for j := 0; j < n; j++ {
|
||||
out[j].setGEJ(&points[j])
|
||||
}
|
||||
}
|
||||
},
|
||||
)
|
||||
|
||||
b.Run(
|
||||
fmt.Sprintf("Batch_%d", n),
|
||||
func(b *testing.B) {
|
||||
out := make([]GroupElementAffine, n)
|
||||
b.ResetTimer()
|
||||
for i := 0; i < b.N; i++ {
|
||||
BatchNormalize(out, points)
|
||||
}
|
||||
},
|
||||
)
|
||||
}
|
||||
}
|
||||
|
||||
260
scalar.go
260
scalar.go
@@ -40,6 +40,66 @@ var (
|
||||
// ScalarOne represents the scalar 1
|
||||
ScalarOne = Scalar{d: [4]uint64{1, 0, 0, 0}}
|
||||
|
||||
// scalarLambda is the GLV endomorphism constant λ (cube root of unity mod n)
|
||||
// λ^3 ≡ 1 (mod n), and λ^2 + λ + 1 ≡ 0 (mod n)
|
||||
// Value: 0x5363AD4CC05C30E0A5261C028812645A122E22EA20816678DF02967C1B23BD72
|
||||
// From libsecp256k1 scalar_impl.h line 81-84
|
||||
scalarLambda = Scalar{
|
||||
d: [4]uint64{
|
||||
0xDF02967C1B23BD72, // limb 0 (least significant)
|
||||
0x122E22EA20816678, // limb 1
|
||||
0xA5261C028812645A, // limb 2
|
||||
0x5363AD4CC05C30E0, // limb 3 (most significant)
|
||||
},
|
||||
}
|
||||
|
||||
// GLV scalar splitting constants from libsecp256k1 scalar_impl.h lines 142-157
|
||||
// These are used in the splitLambda function to decompose a scalar k
|
||||
// into k1 and k2 such that k1 + k2*λ ≡ k (mod n)
|
||||
|
||||
// scalarMinusB1 = -b1 where b1 is from the GLV basis
|
||||
// Value: 0x00000000000000000000000000000000E4437ED6010E88286F547FA90ABFE4C3
|
||||
scalarMinusB1 = Scalar{
|
||||
d: [4]uint64{
|
||||
0x6F547FA90ABFE4C3, // limb 0
|
||||
0xE4437ED6010E8828, // limb 1
|
||||
0x0000000000000000, // limb 2
|
||||
0x0000000000000000, // limb 3
|
||||
},
|
||||
}
|
||||
|
||||
// scalarMinusB2 = -b2 where b2 is from the GLV basis
|
||||
// Value: 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE8A280AC50774346DD765CDA83DB1562C
|
||||
scalarMinusB2 = Scalar{
|
||||
d: [4]uint64{
|
||||
0xD765CDA83DB1562C, // limb 0
|
||||
0x8A280AC50774346D, // limb 1
|
||||
0xFFFFFFFFFFFFFFFE, // limb 2
|
||||
0xFFFFFFFFFFFFFFFF, // limb 3
|
||||
},
|
||||
}
|
||||
|
||||
// scalarG1 is a precomputed constant for scalar splitting: g1 = round(2^384 * b2 / n)
|
||||
// Value: 0x3086D221A7D46BCDE86C90E49284EB153DAA8A1471E8CA7FE893209A45DBB031
|
||||
scalarG1 = Scalar{
|
||||
d: [4]uint64{
|
||||
0xE893209A45DBB031, // limb 0
|
||||
0x3DAA8A1471E8CA7F, // limb 1
|
||||
0xE86C90E49284EB15, // limb 2
|
||||
0x3086D221A7D46BCD, // limb 3
|
||||
},
|
||||
}
|
||||
|
||||
// scalarG2 is a precomputed constant for scalar splitting: g2 = round(2^384 * (-b1) / n)
|
||||
// Value: 0xE4437ED6010E88286F547FA90ABFE4C4221208AC9DF506C61571B4AE8AC47F71
|
||||
scalarG2 = Scalar{
|
||||
d: [4]uint64{
|
||||
0x1571B4AE8AC47F71, // limb 0
|
||||
0x221208AC9DF506C6, // limb 1
|
||||
0x6F547FA90ABFE4C4, // limb 2
|
||||
0xE4437ED6010E8828, // limb 3
|
||||
},
|
||||
}
|
||||
)
|
||||
|
||||
// setInt sets a scalar to a small integer value
|
||||
@@ -755,10 +815,9 @@ func (s *Scalar) wNAF(wnaf []int, w uint) int {
|
||||
var k Scalar
|
||||
k = *s
|
||||
|
||||
// If the scalar is negative, make it positive
|
||||
if k.getBits(255, 1) == 1 {
|
||||
k.negate(&k)
|
||||
}
|
||||
// Note: We do NOT negate the scalar here. The caller is responsible for
|
||||
// ensuring the scalar is in the appropriate form. The ecmultEndoSplit
|
||||
// function already handles sign normalization.
|
||||
|
||||
bits := 0
|
||||
var carry uint32
|
||||
@@ -785,12 +844,203 @@ func (s *Scalar) wNAF(wnaf []int, w uint) int {
|
||||
word -= carry << window
|
||||
|
||||
// word is now in range [-(2^(w-1)-1), 2^(w-1)-1]
|
||||
wnaf[bit] = int(word)
|
||||
// Convert through int32 to properly handle negative values
|
||||
wnaf[bit] = int(int32(word))
|
||||
bits = bit + int(window) - 1
|
||||
|
||||
bit += int(window)
|
||||
}
|
||||
|
||||
// Handle remaining carry at bit 256
|
||||
// This can happen for scalars where the wNAF representation extends to 257 bits
|
||||
if carry != 0 {
|
||||
wnaf[256] = int(carry)
|
||||
bits = 256
|
||||
}
|
||||
|
||||
return bits + 1
|
||||
}
|
||||
|
||||
// wNAFSigned converts a scalar to Windowed Non-Adjacent Form representation,
|
||||
// handling sign normalization. If the scalar has its high bit set (is "negative"
|
||||
// in the modular sense), it will be negated and the negated flag will be true.
|
||||
//
|
||||
// Returns the number of digits and whether the scalar was negated.
|
||||
// The caller must negate the result point if negated is true.
|
||||
func (s *Scalar) wNAFSigned(wnaf []int, w uint) (int, bool) {
|
||||
if w < 2 || w > 31 {
|
||||
panic("w must be between 2 and 31")
|
||||
}
|
||||
if len(wnaf) < 257 {
|
||||
panic("wnaf slice must have at least 257 elements")
|
||||
}
|
||||
|
||||
var k Scalar
|
||||
k = *s
|
||||
|
||||
// If the scalar has high bit set, negate it
|
||||
negated := false
|
||||
if k.getBits(255, 1) == 1 {
|
||||
k.negate(&k)
|
||||
negated = true
|
||||
}
|
||||
|
||||
bits := k.wNAF(wnaf, w)
|
||||
return bits, negated
|
||||
}
|
||||
|
||||
// =============================================================================
|
||||
// GLV Endomorphism Support Functions
|
||||
// =============================================================================
|
||||
|
||||
// caddBit conditionally adds a power of 2 to the scalar
|
||||
// If flag is non-zero, adds 2^bit to r
|
||||
func (r *Scalar) caddBit(bit uint, flag int) {
|
||||
if flag == 0 {
|
||||
return
|
||||
}
|
||||
|
||||
limbIdx := bit >> 6 // bit / 64
|
||||
bitIdx := bit & 0x3F // bit % 64
|
||||
addVal := uint64(1) << bitIdx
|
||||
|
||||
var carry uint64
|
||||
if limbIdx == 0 {
|
||||
r.d[0], carry = bits.Add64(r.d[0], addVal, 0)
|
||||
r.d[1], carry = bits.Add64(r.d[1], 0, carry)
|
||||
r.d[2], carry = bits.Add64(r.d[2], 0, carry)
|
||||
r.d[3], _ = bits.Add64(r.d[3], 0, carry)
|
||||
} else if limbIdx == 1 {
|
||||
r.d[1], carry = bits.Add64(r.d[1], addVal, 0)
|
||||
r.d[2], carry = bits.Add64(r.d[2], 0, carry)
|
||||
r.d[3], _ = bits.Add64(r.d[3], 0, carry)
|
||||
} else if limbIdx == 2 {
|
||||
r.d[2], carry = bits.Add64(r.d[2], addVal, 0)
|
||||
r.d[3], _ = bits.Add64(r.d[3], 0, carry)
|
||||
} else if limbIdx == 3 {
|
||||
r.d[3], _ = bits.Add64(r.d[3], addVal, 0)
|
||||
}
|
||||
}
|
||||
|
||||
// mulShiftVar computes r = round((a * b) >> shift) for shift >= 256
|
||||
// This is used in GLV scalar splitting to compute c1 = round(k * g1 / 2^384)
|
||||
// The rounding is achieved by adding the bit just below the shift position
|
||||
func (r *Scalar) mulShiftVar(a, b *Scalar, shift uint) {
|
||||
if shift < 256 {
|
||||
panic("mulShiftVar requires shift >= 256")
|
||||
}
|
||||
|
||||
// Compute full 512-bit product
|
||||
var l [8]uint64
|
||||
r.mul512(l[:], a, b)
|
||||
|
||||
// Extract bits [shift, shift+256) from the 512-bit product
|
||||
shiftLimbs := shift >> 6 // Number of full 64-bit limbs to skip
|
||||
shiftLow := shift & 0x3F // Bit offset within the limb
|
||||
shiftHigh := 64 - shiftLow // Complementary shift for combining limbs
|
||||
|
||||
// Extract each limb of the result
|
||||
// For shift=384, shiftLimbs=6, shiftLow=0
|
||||
// r.d[0] = l[6], r.d[1] = l[7], r.d[2] = 0, r.d[3] = 0
|
||||
|
||||
if shift < 512 {
|
||||
if shiftLow != 0 {
|
||||
r.d[0] = (l[shiftLimbs] >> shiftLow) | (l[shiftLimbs+1] << shiftHigh)
|
||||
} else {
|
||||
r.d[0] = l[shiftLimbs]
|
||||
}
|
||||
} else {
|
||||
r.d[0] = 0
|
||||
}
|
||||
|
||||
if shift < 448 {
|
||||
if shiftLow != 0 && shift < 384 {
|
||||
r.d[1] = (l[shiftLimbs+1] >> shiftLow) | (l[shiftLimbs+2] << shiftHigh)
|
||||
} else if shiftLow != 0 {
|
||||
r.d[1] = l[shiftLimbs+1] >> shiftLow
|
||||
} else {
|
||||
r.d[1] = l[shiftLimbs+1]
|
||||
}
|
||||
} else {
|
||||
r.d[1] = 0
|
||||
}
|
||||
|
||||
if shift < 384 {
|
||||
if shiftLow != 0 && shift < 320 {
|
||||
r.d[2] = (l[shiftLimbs+2] >> shiftLow) | (l[shiftLimbs+3] << shiftHigh)
|
||||
} else if shiftLow != 0 {
|
||||
r.d[2] = l[shiftLimbs+2] >> shiftLow
|
||||
} else {
|
||||
r.d[2] = l[shiftLimbs+2]
|
||||
}
|
||||
} else {
|
||||
r.d[2] = 0
|
||||
}
|
||||
|
||||
if shift < 320 {
|
||||
r.d[3] = l[shiftLimbs+3] >> shiftLow
|
||||
} else {
|
||||
r.d[3] = 0
|
||||
}
|
||||
|
||||
// Round by adding the bit just below the shift position
|
||||
// This implements round() instead of floor()
|
||||
roundBit := int((l[(shift-1)>>6] >> ((shift - 1) & 0x3F)) & 1)
|
||||
r.caddBit(0, roundBit)
|
||||
}
|
||||
|
||||
// splitLambda decomposes scalar k into k1, k2 such that k1 + k2*λ ≡ k (mod n)
|
||||
// where k1 and k2 are approximately 128 bits each.
|
||||
// This is the core of the GLV endomorphism optimization.
|
||||
//
|
||||
// The algorithm uses precomputed constants g1, g2 to compute:
|
||||
// c1 = round(k * g1 / 2^384)
|
||||
// c2 = round(k * g2 / 2^384)
|
||||
// k2 = c1*(-b1) + c2*(-b2)
|
||||
// k1 = k - k2*λ
|
||||
//
|
||||
// Reference: libsecp256k1 scalar_impl.h:secp256k1_scalar_split_lambda
|
||||
func scalarSplitLambda(r1, r2, k *Scalar) {
|
||||
var c1, c2 Scalar
|
||||
|
||||
// c1 = round(k * g1 / 2^384)
|
||||
c1.mulShiftVar(k, &scalarG1, 384)
|
||||
|
||||
// c2 = round(k * g2 / 2^384)
|
||||
c2.mulShiftVar(k, &scalarG2, 384)
|
||||
|
||||
// c1 = c1 * (-b1)
|
||||
c1.mul(&c1, &scalarMinusB1)
|
||||
|
||||
// c2 = c2 * (-b2)
|
||||
c2.mul(&c2, &scalarMinusB2)
|
||||
|
||||
// r2 = c1 + c2
|
||||
r2.add(&c1, &c2)
|
||||
|
||||
// r1 = r2 * λ
|
||||
r1.mul(r2, &scalarLambda)
|
||||
|
||||
// r1 = -r1
|
||||
r1.negate(r1)
|
||||
|
||||
// r1 = k + (-r2*λ) = k - r2*λ
|
||||
r1.add(r1, k)
|
||||
}
|
||||
|
||||
// scalarSplit128 splits a scalar into two 128-bit halves
|
||||
// r1 = k & ((1 << 128) - 1) (low 128 bits)
|
||||
// r2 = k >> 128 (high 128 bits)
|
||||
// This is used for generator multiplication optimization
|
||||
func scalarSplit128(r1, r2, k *Scalar) {
|
||||
r1.d[0] = k.d[0]
|
||||
r1.d[1] = k.d[1]
|
||||
r1.d[2] = 0
|
||||
r1.d[3] = 0
|
||||
|
||||
r2.d[0] = k.d[2]
|
||||
r2.d[1] = k.d[3]
|
||||
r2.d[2] = 0
|
||||
r2.d[3] = 0
|
||||
}
|
||||
|
||||
|
||||
Reference in New Issue
Block a user