p256k1/OPTIMIZATION_SUMMARY.md

secp256k1 Go Implementation - Optimization Summary

Overview

This document summarizes the optimizations implemented in the Go port of secp256k1, focusing on performance-critical cryptographic operations.

Implemented Optimizations

1. SHA-256 SIMD Implementation

• Library: github.com/minio/sha256-simd
• Performance: ~61.56 ns/op for basic SHA-256 operations
• Features:
  • Hardware-accelerated SHA-256 when available
  • Tagged SHA-256 for BIP-340 compatibility
  • HMAC-SHA256 for RFC 6979 nonce generation

2. Optimized Scalar Multiplication

Generator Multiplication (ecmultGen)

• Method: Precomputed windowed tables
• Window Size: 4 bits (16 precomputed points per window)
• Table Size: 64 windows × 16 points = 1,024 precomputed points
• Performance: ~720.2 ns/op (significant improvement over naive methods)
• Memory: ~65KB for precomputed table

Constant-Time Multiplication (EcmultConst)

• Method: Windowed method with odd multiples
• Window Size: 4 bits
• Performance: ~8,636 ns/op
• Security: Constant-time execution to prevent side-channel attacks

Multi-Scalar Multiplication

• Methods:
  • EcmultMulti: Simple approach for multiple point multiplications
  • EcmultStrauss: Interleaved binary method for better efficiency
• Use Case: Batch verification and complex cryptographic protocols

3. RFC 6979 Deterministic Nonce Generation

• Standard: RFC 6979 compliant
• Implementation: HMAC-SHA256 based
• Performance: ~3,092 ns/op
• Security: Deterministic, no random number generator dependency
• Features:
  • Proper HMAC key derivation
  • Support for additional entropy
  • Algorithm identifier support

4. Side-Channel Protection

Context Blinding

• Purpose: Protection against side-channel attacks
• Method: Random blinding of precomputed tables
• Implementation: Blinding points added to computation results
• Security: Makes timing attacks significantly harder

Constant-Time Operations

• Field Operations: Magnitude tracking and normalization
• Scalar Operations: Constant-time conditional operations
• Group Operations: Unified addition formulas where possible

Performance Benchmarks

BenchmarkOptimizedEcmultGen-12      	 1671268	       720.2 ns/op
BenchmarkEcmultConst-12             	  139990	      8636 ns/op
BenchmarkSHA256-12                  	19563603	        61.56 ns/op
BenchmarkTaggedSHA256-12            	 4350244	       275.7 ns/op
BenchmarkRFC6979Nonce-12            	  367168	      3092 ns/op
BenchmarkFieldAddition-12           	518004895	         2.358 ns/op
BenchmarkScalarMultiplication-12    	124707854	         9.791 ns/op

Memory Usage

Precomputed Tables

• Generator Table: ~65KB (64 windows × 16 points × ~64 bytes per point)
• General Multiplication: Dynamic table generation as needed
• Total Context Size: ~66KB including blinding and metadata

Optimization Trade-offs

• Memory vs Speed: Precomputed tables use significant memory for speed gains
• Security vs Performance: Constant-time operations are slower but secure
• Determinism vs Randomness: RFC 6979 provides determinism without entropy requirements

Advanced Features

Endomorphism Optimization (Prepared)

• secp256k1 Specific: Efficiently computable endomorphism
• Method: Split scalar multiplication into two half-size operations
• Status: Framework implemented, full optimization pending
• Potential Gain: ~40% speedup for scalar multiplication

Precomputed Point Tables

• Structure: Hierarchical windowed tables
• Flexibility: Configurable window sizes for memory/speed trade-offs
• Scalability: Supports both small embedded and high-performance scenarios

Security Considerations

Constant-Time Guarantees

• Field Arithmetic: Magnitude-based normalization prevents timing leaks
• Scalar Operations: Conditional moves instead of branches
• Point Operations: Unified addition formulas

Side-Channel Resistance

• Blinding: Random blinding of intermediate values
• Table Access: Constant-time table lookups where possible
• Memory Access: Predictable access patterns

Cryptographic Correctness

• Field Reduction: Proper modular arithmetic
• Group Law: Correct elliptic curve point operations
• Scalar Arithmetic: Proper modular arithmetic modulo curve order

Future Optimizations

Potential Improvements

1. Assembly Optimizations: Hand-optimized assembly for critical paths
2. SIMD Field Arithmetic: Vectorized field operations
3. Batch Operations: Optimized batch verification
4. Memory Layout: Cache-friendly data structures
5. Endomorphism: Full GLV/GLS endomorphism implementation

Platform-Specific Optimizations

• x86_64: AVX2/AVX-512 vectorization
• ARM64: NEON vectorization
• Hardware Acceleration: Dedicated crypto instructions where available

Conclusion

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.

Key achievements:

• ✅ 720ns generator multiplication (vs. several microseconds for naive implementation)
• ✅ Hardware-accelerated SHA-256
• ✅ RFC 6979 compliant nonce generation
• ✅ Side-channel resistant implementations
• ✅ Comprehensive test coverage
• ✅ Benchmark suite for performance monitoring

The implementation is now suitable for production use in performance-critical applications while maintaining the security properties required for cryptographic operations.