secp256k1 Go Implementation

This package provides a pure Go implementation of the secp256k1 elliptic curve cryptographic primitives, ported from the libsecp256k1 C library.

Features Implemented

✅ Core Components

• Field Arithmetic (field.go, field_mul.go): Complete implementation of field operations modulo the secp256k1 field prime (2^256 - 2^32 - 977)

  • 5x52-bit limb representation for efficient arithmetic
  • Addition, multiplication, squaring, inversion operations
  • Constant-time normalization and magnitude management

• Scalar Arithmetic (scalar.go): Complete implementation of scalar operations modulo the group order

  • 4x64-bit limb representation
  • Addition, multiplication, inversion, negation operations
  • Proper overflow handling and reduction

• Group Operations (group.go): Elliptic curve point operations

  • Affine and Jacobian coordinate representations
  • Point addition, doubling, negation
  • Coordinate conversion between representations

• Context Management (context.go): Context objects for enhanced security

  • Context creation, cloning, destruction
  • Randomization for side-channel protection
  • Callback management for error handling

• Main API (secp256k1.go): Core secp256k1 API functions

  • Public key parsing, serialization, and comparison
  • ECDSA signature parsing and serialization
  • Key generation and verification
  • Basic ECDSA signing and verification (simplified implementation)

• Utilities (util.go): Helper functions and constants

  • Memory management utilities
  • Endianness conversion functions
  • Bit manipulation utilities
  • Error handling and callbacks

✅ Testing

• Comprehensive test suite (secp256k1_test.go) covering:
  • Basic functionality and self-tests
  • Field element operations
  • Scalar operations
  • Key generation
  • Signature operations
  • Public key operations
  • Performance benchmarks

Usage

package main

import (
    "fmt"
    "crypto/rand"
    p256k1 "p256k1.mleku.dev/pkg"
)

func main() {
    // Create context
    ctx, err := p256k1.ContextCreate(p256k1.ContextNone)
    if err != nil {
        panic(err)
    }
    defer p256k1.ContextDestroy(ctx)
    
    // Generate secret key
    var seckey [32]byte
    rand.Read(seckey[:])
    
    // Verify secret key
    if !p256k1.ECSecKeyVerify(ctx, seckey[:]) {
        panic("Invalid secret key")
    }
    
    // Create public key
    var pubkey p256k1.PublicKey
    if !p256k1.ECPubkeyCreate(ctx, &pubkey, seckey[:]) {
        panic("Failed to create public key")
    }
    
    fmt.Println("Successfully created secp256k1 key pair!")
}

Architecture

The implementation follows the same architectural patterns as libsecp256k1:

1. Layered Design: Low-level field/scalar arithmetic → Group operations → High-level API
2. Constant-Time Operations: Designed to prevent timing side-channel attacks
3. Magnitude Tracking: Field elements track their "magnitude" to optimize operations
4. Context Objects: Encapsulate state and provide enhanced security features

Performance

Benchmark results on AMD Ryzen 5 PRO 4650G:

• Field Addition: ~2.4 ns/op
• Scalar Multiplication: ~9.9 ns/op

Implementation Status

✅ Completed

• Core field and scalar arithmetic
• Basic group operations
• Context management
• Main API structure
• Key generation and verification
• Basic signature operations
• Comprehensive test suite

🚧 Simplified/Placeholder

• ECDSA Implementation: Basic structure in place, but signing/verification uses simplified algorithms
• Field Multiplication: Uses simplified approach instead of optimized assembly
• Point Validation: Curve equation checking is simplified
• Nonce Generation: Uses crypto/rand instead of RFC 6979

❌ Not Yet Implemented

• Hash Functions: SHA-256 and tagged hash implementations
• Optimized Multiplication: Full constant-time field multiplication
• Precomputed Tables: Optimized scalar multiplication with precomputed points
• Optional Modules: Schnorr signatures, ECDH, extra keys
• Recovery: Public key recovery from signatures
• Complete ECDSA: Full constant-time ECDSA implementation

Security Considerations

⚠️ This implementation is for educational/development purposes and should not be used in production without further security review and completion of the cryptographic implementations.

Key security features implemented:

• Constant-time field operations (basic level)
• Magnitude tracking to prevent overflows
• Memory clearing for sensitive data
• Context randomization support

Key security features still needed:

• Complete constant-time ECDSA implementation
• Proper nonce generation (RFC 6979)
• Side-channel resistance verification
• Comprehensive security testing

Building and Testing

cd pkg/
go test -v          # Run all tests
go test -bench=.    # Run benchmarks
go build            # Build the package

License

This implementation is derived from libsecp256k1 and maintains the same MIT license.