144 lines
5.7 KiB
Markdown
144 lines
5.7 KiB
Markdown
# secp256k1 Go Implementation - Optimization Summary
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## Overview
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This document summarizes the optimizations implemented in the Go port of secp256k1, focusing on performance-critical cryptographic operations.
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## Implemented Optimizations
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### 1. SHA-256 SIMD Implementation
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- **Library**: `github.com/minio/sha256-simd`
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- **Performance**: ~61.56 ns/op for basic SHA-256 operations
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- **Features**:
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- Hardware-accelerated SHA-256 when available
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- Tagged SHA-256 for BIP-340 compatibility
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- HMAC-SHA256 for RFC 6979 nonce generation
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### 2. Optimized Scalar Multiplication
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#### Generator Multiplication (`ecmultGen`)
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- **Method**: Precomputed windowed tables
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- **Window Size**: 4 bits (16 precomputed points per window)
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- **Table Size**: 64 windows × 16 points = 1,024 precomputed points
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- **Performance**: ~720.2 ns/op (significant improvement over naive methods)
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- **Memory**: ~65KB for precomputed table
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#### Constant-Time Multiplication (`EcmultConst`)
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- **Method**: Windowed method with odd multiples
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- **Window Size**: 4 bits
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- **Performance**: ~8,636 ns/op
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- **Security**: Constant-time execution to prevent side-channel attacks
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#### Multi-Scalar Multiplication
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- **Methods**:
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- `EcmultMulti`: Simple approach for multiple point multiplications
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- `EcmultStrauss`: Interleaved binary method for better efficiency
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- **Use Case**: Batch verification and complex cryptographic protocols
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### 3. RFC 6979 Deterministic Nonce Generation
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- **Standard**: RFC 6979 compliant
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- **Implementation**: HMAC-SHA256 based
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- **Performance**: ~3,092 ns/op
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- **Security**: Deterministic, no random number generator dependency
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- **Features**:
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- Proper HMAC key derivation
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- Support for additional entropy
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- Algorithm identifier support
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### 4. Side-Channel Protection
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#### Context Blinding
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- **Purpose**: Protection against side-channel attacks
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- **Method**: Random blinding of precomputed tables
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- **Implementation**: Blinding points added to computation results
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- **Security**: Makes timing attacks significantly harder
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#### Constant-Time Operations
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- **Field Operations**: Magnitude tracking and normalization
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- **Scalar Operations**: Constant-time conditional operations
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- **Group Operations**: Unified addition formulas where possible
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## Performance Benchmarks
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```
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BenchmarkOptimizedEcmultGen-12 1671268 720.2 ns/op
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BenchmarkEcmultConst-12 139990 8636 ns/op
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BenchmarkSHA256-12 19563603 61.56 ns/op
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BenchmarkTaggedSHA256-12 4350244 275.7 ns/op
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BenchmarkRFC6979Nonce-12 367168 3092 ns/op
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BenchmarkFieldAddition-12 518004895 2.358 ns/op
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BenchmarkScalarMultiplication-12 124707854 9.791 ns/op
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```
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## Memory Usage
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### Precomputed Tables
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- **Generator Table**: ~65KB (64 windows × 16 points × ~64 bytes per point)
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- **General Multiplication**: Dynamic table generation as needed
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- **Total Context Size**: ~66KB including blinding and metadata
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### Optimization Trade-offs
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- **Memory vs Speed**: Precomputed tables use significant memory for speed gains
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- **Security vs Performance**: Constant-time operations are slower but secure
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- **Determinism vs Randomness**: RFC 6979 provides determinism without entropy requirements
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## Advanced Features
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### Endomorphism Optimization (Prepared)
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- **secp256k1 Specific**: Efficiently computable endomorphism
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- **Method**: Split scalar multiplication into two half-size operations
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- **Status**: Framework implemented, full optimization pending
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- **Potential Gain**: ~40% speedup for scalar multiplication
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### Precomputed Point Tables
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- **Structure**: Hierarchical windowed tables
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- **Flexibility**: Configurable window sizes for memory/speed trade-offs
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- **Scalability**: Supports both small embedded and high-performance scenarios
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## Security Considerations
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### Constant-Time Guarantees
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- **Field Arithmetic**: Magnitude-based normalization prevents timing leaks
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- **Scalar Operations**: Conditional moves instead of branches
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- **Point Operations**: Unified addition formulas
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### Side-Channel Resistance
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- **Blinding**: Random blinding of intermediate values
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- **Table Access**: Constant-time table lookups where possible
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- **Memory Access**: Predictable access patterns
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### Cryptographic Correctness
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- **Field Reduction**: Proper modular arithmetic
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- **Group Law**: Correct elliptic curve point operations
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- **Scalar Arithmetic**: Proper modular arithmetic modulo curve order
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## Future Optimizations
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### Potential Improvements
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1. **Assembly Optimizations**: Hand-optimized assembly for critical paths
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2. **SIMD Field Arithmetic**: Vectorized field operations
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3. **Batch Operations**: Optimized batch verification
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4. **Memory Layout**: Cache-friendly data structures
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5. **Endomorphism**: Full GLV/GLS endomorphism implementation
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### Platform-Specific Optimizations
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- **x86_64**: AVX2/AVX-512 vectorization
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- **ARM64**: NEON vectorization
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- **Hardware Acceleration**: Dedicated crypto instructions where available
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## Conclusion
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The Go implementation now includes significant performance optimizations while maintaining security and correctness. The precomputed table approach provides substantial speedups for the most common operations (generator multiplication), while constant-time implementations ensure security against side-channel attacks.
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Key achievements:
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- ✅ 720ns generator multiplication (vs. several microseconds for naive implementation)
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- ✅ Hardware-accelerated SHA-256
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- ✅ RFC 6979 compliant nonce generation
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- ✅ Side-channel resistant implementations
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- ✅ Comprehensive test coverage
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- ✅ Benchmark suite for performance monitoring
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The implementation is now suitable for production use in performance-critical applications while maintaining the security properties required for cryptographic operations.
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