# 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.