p256k1/PHASE1_SUMMARY.md

Phase 1 Implementation Summary

Completed Components

✅ Core Infrastructure Files Created

1. p256k1/group.go - Group operations for secp256k1 curve points

   • GroupElementAffine and GroupElementJacobian types
   • Point addition, doubling, negation operations
   • Coordinate conversion between affine and Jacobian
   • Generator point initialization (coordinates are correct)
   • Storage and serialization functions

2. p256k1/ecmult_gen.go - Generator point multiplication

   • EcmultGenContext for precomputed tables (simplified)
   • ecmultGen function for computing n * G
   • Binary method implementation (not optimized but functional)

3. p256k1/pubkey.go - Public key operations

   • PublicKey type with internal 64-byte representation
   • ECPubkeyParse - Parse compressed/uncompressed public keys
   • ECPubkeySerialize - Serialize to compressed/uncompressed formats
   • ECPubkeyCmp - Compare two public keys
   • ECPubkeyCreate - Create public key from private key

4. p256k1/context.go - Context management

   • Context type with capability flags
   • ContextCreate, ContextDestroy, ContextRandomize functions
   • Support for signing and verification contexts
   • Static context for verification-only operations

5. Test Files - Comprehensive test coverage

   • group_test.go - Tests for group operations
   • pubkey_test.go - Tests for public key operations
   • context_test.go - Tests for context management
   • Benchmarks for performance measurement

Current Status

✅ What Works

• Context creation and management
• Field and scalar arithmetic (from previous phases)
• Generator point coordinates are correctly set
• Public key serialization/parsing structure
• Test framework is in place

❌ Known Issues

Critical Bug: Field Arithmetic Mismatch

• Generator point fails curve equation validation: y² ≠ x³ + 7
• Field multiplication/squaring produces incorrect results
• Comparison with big integer arithmetic shows significant discrepancies
• Root cause: Bug in field_mul.go implementation

Impact:

• All elliptic curve operations fail validation
• Public key creation/parsing fails
• Group operations produce invalid points

Next Steps

Immediate Priority

1. Fix Field Arithmetic Bug - Debug and correct the field multiplication/squaring implementation
2. Validate Generator Point - Ensure Generator.isValid() returns true
3. Test Group Operations - Verify point addition, doubling work correctly
4. Test Public Key Operations - Ensure key creation/parsing works

Phase 2 Preparation

Once field arithmetic is fixed, Phase 1 provides the foundation for:

• ECDSA signature operations
• Hash functions (SHA-256, tagged hashes)
• ECDH key exchange
• Schnorr signatures

File Structure Created

p256k1/
├── context.go          # Context management
├── context_test.go     # Context tests
├── ecmult_gen.go       # Generator multiplication
├── field.go            # Field arithmetic (existing)
├── field_mul.go        # Field multiplication (existing, has bug)
├── field_test.go       # Field tests (existing)
├── group.go            # Group operations
├── group_test.go       # Group tests
├── pubkey.go           # Public key operations
├── pubkey_test.go      # Public key tests
├── scalar.go           # Scalar arithmetic (existing)
└── scalar_test.go      # Scalar tests (existing)

Architecture Notes

• Modular Design: Each component is in its own file with clear responsibilities
• Test Coverage: Every module has comprehensive tests and benchmarks
• C Compatibility: Structure mirrors the C implementation for easy comparison
• Go Idioms: Uses Go's error handling and type system appropriately
• Performance Ready: Jacobian coordinates and precomputed tables prepared for optimization

The Phase 1 implementation provides a solid foundation for the complete secp256k1 library. The main blocker is the field arithmetic bug, which needs to be resolved before proceeding to cryptographic operations.