# 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.