# Four-Phase Implementation Plan - secp256k1 Go Port

## Overview

This document outlines the complete four-phase implementation plan for porting the secp256k1 cryptographic library from C to Go. The implementation follows the C reference implementation exactly, ensuring mathematical correctness and compatibility.

---

## Phase 1: Core Infrastructure & Mathematical Primitives ✅

### Status: **100% Complete** (25/25 tests passing)

### Objectives
Establish the mathematical foundation and core infrastructure for all cryptographic operations.

### Completed Components

#### 1. **Field Element Operations** ✅
- **File**: `field.go`, `field_mul.go`, `field_test.go`
- **Status**: 100% complete (9/9 tests passing)
- **Key Features**:
  - Field arithmetic (addition, subtraction, multiplication, squaring)
  - Field normalization and reduction
  - Field inverse computation (Fermat's little theorem)
  - Field square root computation
  - 512-bit to 256-bit modular reduction (matches C reference exactly)
  - Constant-time operations where required
  - Secure memory clearing

#### 2. **Scalar Operations** ✅
- **File**: `scalar.go`, `scalar_test.go`
- **Status**: 100% complete (11/11 tests passing)
- **Key Features**:
  - Scalar arithmetic (addition, subtraction, multiplication)
  - Scalar modular inverse
  - Scalar exponentiation
  - Scalar halving
  - 512-bit to 256-bit modular reduction (three-stage reduction from C)
  - Private key validation
  - Constant-time conditional operations

#### 3. **Context Management** ✅
- **File**: `context.go`, `context_test.go`
- **Status**: 100% complete (5/5 tests passing)
- **Key Features**:
  - Context creation with capability flags (signing/verification)
  - Context destruction and cleanup
  - Context randomization for side-channel protection
  - Static verification-only context
  - Capability checking

#### 4. **Group Operations** ✅
- **File**: `group.go`, `group_test.go`
- **Status**: 100% complete (4/4 tests passing)
- **Key Features**:
  - `GroupElementAffine` and `GroupElementJacobian` types
  - Affine coordinate operations (complete)
  - Jacobian coordinate operations (optimized)
  - Point doubling (`double`) - C reference implementation
  - Point addition in Jacobian coordinates (`addVar`) - C reference implementation (~78x faster)
  - Point addition with affine input (`addGE`) - C reference implementation (optimized)
  - Coordinate conversion (affine ↔ Jacobian)
  - Generator point initialization
  - Storage format conversion
  - Field element `normalizesToZeroVar` helper for efficient point comparison

#### 5. **Public Key Operations** ✅
- **File**: `pubkey.go`, `pubkey_test.go`
- **Status**: 100% complete (4/4 tests passing)
- **Key Features**:
  - `PublicKey` type with 64-byte internal representation
  - Public key parsing (compressed/uncompressed)
  - Public key serialization
  - Public key comparison (working)
  - Public key creation from private key (scalar multiplication working)

#### 6. **Generator Multiplication** ✅
- **File**: `ecmult_gen.go`
- **Status**: Infrastructure complete
- **Key Features**:
  - `EcmultGenContext` for precomputed tables
  - `EcmultGen` function for `n * G` computation
  - Binary method implementation (ready for optimization)

### Remaining Issues

None - Phase 1 is complete! ✅

### Test Coverage
- **Total Tests**: 25 test functions
- **Passing**: 25 tests ✅
- **Failing**: 0 tests ✅
- **Success Rate**: 100%

### Files Created
```
├── context.go          ✅ Context management (COMPLETE)
├── context_test.go     ✅ Context tests (ALL PASSING)
├── field.go            ✅ Field arithmetic (COMPLETE)
├── field_mul.go        ✅ Field multiplication/operations (COMPLETE)
├── field_test.go       ✅ Field tests (ALL PASSING)
├── scalar.go           ✅ Scalar arithmetic (COMPLETE)
├── scalar_test.go      ✅ Scalar tests (ALL PASSING)
├── group.go            ✅ Group operations (COMPLETE)
├── group_test.go       ✅ Group tests (ALL PASSING)
├── ecmult_gen.go       ✅ Generator multiplication (INFRASTRUCTURE)
├── pubkey.go           ✅ Public key operations (COMPLETE)
└── pubkey_test.go      ✅ Public key tests (ALL PASSING)
```

---

## Phase 2: ECDSA Signatures & Hash Functions ✅

### Status: **100% Complete**

### Objectives
Implement ECDSA signature creation and verification, along with cryptographic hash functions.

### Planned Components

#### 1. **Hash Functions** ✅
- **Files**: `hash.go`, `hash_test.go`
- **Status**: 100% complete
- **Key Features**:
  - SHA-256 implementation (using sha256-simd)
  - Tagged SHA-256 (BIP-340 style)
  - RFC6979 nonce generation (deterministic signing)
  - HMAC-SHA256 implementation
  - Hash-to-field element conversion
  - Hash-to-scalar conversion
  - Message hashing utilities

#### 2. **ECDSA Signatures** ✅
- **Files**: `ecdsa.go`, `ecdsa_test.go`
- **Status**: 100% complete
- **Key Features**:
  - `ECDSASign` - Create signatures from message hash and private key
  - `ECDSAVerify` - Verify signatures against message hash and public key
  - Compact signature format (64-byte)
  - Signature normalization (low-S)
  - RFC6979 deterministic nonce generation

#### 3. **Private Key Operations** ✅
- **Files**: `eckey.go`, `eckey_test.go`
- **Status**: 100% complete
- **Key Features**:
  - Private key generation (`ECSeckeyGenerate`)
  - Private key validation (`ECSeckeyVerify`)
  - Private key negation (`ECSeckeyNegate`)
  - Key pair generation (`ECKeyPairGenerate`)
  - Key tweaking (add/multiply) for BIP32-style derivation
  - Public key tweaking (add/multiply)

#### 4. **Benchmarks**
- **Files**: `ecdsa_bench_test.go`, `BENCHMARK_RESULTS.md`
- **Features**:
  - Signing performance benchmarks ✅
  - Verification performance benchmarks ✅
  - Hash function benchmarks ✅
  - Key generation benchmarks ✅
  - Comparison with C implementation ✅
  - Memory usage profiling ✅
  - Comprehensive benchmark results document ✅

### Dependencies
- ✅ Phase 1: Field arithmetic, scalar arithmetic, group operations
- ✅ Point doubling algorithm working correctly
- ✅ Scalar multiplication working correctly

### Success Criteria
- [x] All ECDSA signing tests pass ✅
- [x] All ECDSA verification tests pass ✅
- [x] Hash functions match reference implementation ✅
- [x] RFC6979 nonce generation produces correct results ✅
- [x] Performance benchmarks implemented and documented ✅
  - Signing: ~5ms/op (2-3x slower than C, acceptable for production)
  - Verification: ~10ms/op (2-3x slower than C, zero allocations)
  - Full benchmark suite: 17 benchmarks covering all operations

---

## Phase 3: ECDH Key Exchange ✅

### Status: **100% Complete**

### Objectives
Implement Elliptic Curve Diffie-Hellman key exchange for secure key derivation.

### Completed Components

#### 1. **ECDH Operations** ✅
- **Files**: `ecdh.go`, `ecdh_test.go`
- **Status**: 100% complete
- **Key Features**:
  - `ECDH` - Compute shared secret from private key and public key ✅
  - `ECDHWithHKDF` - ECDH with HKDF key derivation ✅
  - `ECDHXOnly` - X-only ECDH (BIP-340 style) ✅
  - Custom hash function support ✅
  - Secure memory clearing ✅

#### 2. **Advanced Point Multiplication** ✅
- **Files**: `ecdh.go` (includes EcmultConst and Ecmult)
- **Status**: 100% complete
- **Key Features**:
  - `EcmultConst` - Constant-time multiplication for arbitrary points ✅
  - `Ecmult` - Variable-time optimized multiplication ✅
  - Binary method implementation (ready for further optimization) ✅

#### 3. **HKDF Support** ✅
- **Files**: `ecdh.go`
- **Status**: 100% complete
- **Key Features**:
  - `HKDF` - HMAC-based Key Derivation Function (RFC 5869) ✅
  - Extract and Expand phases ✅
  - Supports arbitrary output length ✅
  - Secure memory clearing ✅

### Dependencies
- ✅ Phase 1: Group operations, scalar multiplication
- ✅ Phase 2: Hash functions (for HKDF)

### Success Criteria
- [x] ECDH computes correct shared secrets ✅
- [x] X-only ECDH matches reference implementation ✅
- [x] HKDF key derivation works correctly ✅
- [x] All ECDH tests pass ✅

---

## Phase 4: Schnorr Signatures & Advanced Features ✅

### Status: **100% Complete**

### Objectives
Implement BIP-340 Schnorr signatures and advanced cryptographic features.

### Completed Components

#### 1. **Schnorr Signatures** ✅
- **Files**: `schnorr.go`, `schnorr_test.go`
- **Status**: 100% complete
- **Key Features**:
  - `SchnorrSign` - Create BIP-340 compliant signatures ✅
  - `SchnorrVerify` - Verify BIP-340 signatures ✅
  - `NonceFunctionBIP340` - BIP-340 nonce generation ✅
  - Tagged hash support (BIP-340 style) ✅
  - Auxiliary randomness support ✅
  - Secure memory clearing ✅

#### 2. **Extended Public Keys** ✅
- **Files**: `extrakeys.go`, `extrakeys_test.go`
- **Status**: 100% complete
- **Key Features**:
  - `XOnlyPubkey` type (32-byte X coordinate) ✅
  - `KeyPair` type for Schnorr signatures ✅
  - `XOnlyPubkeyParse` - Parse x-only public keys ✅
  - `XOnlyPubkeyFromPubkey` - Convert full pubkey to x-only ✅
  - `XOnlyPubkeyCmp` - Compare x-only public keys ✅
  - `KeyPairCreate` - Create keypair from secret key ✅
  - `KeyPairGenerate` - Generate random keypair ✅
  - Public key parity extraction ✅

### Dependencies
- ✅ Phase 1: Complete core infrastructure
- ✅ Phase 2: Hash functions (TaggedHash already implemented)
- ✅ Phase 3: ECDH, optimized multiplication

### Success Criteria
- [x] Schnorr signatures match BIP-340 specification ✅
- [x] All Schnorr signature tests pass ✅
- [x] X-only public keys work correctly ✅
- [x] Keypair operations work correctly ✅
- [x] All Phase 4 tests pass ✅

---

## Overall Implementation Strategy

### Principles
1. **Exact C Reference**: Follow C implementation algorithms exactly
2. **Test-Driven**: Write comprehensive tests for each component
3. **Incremental**: Complete each phase before moving to next
4. **Performance**: Optimize where possible without sacrificing correctness
5. **Go Idioms**: Use Go's type system and error handling appropriately

### Testing Strategy
- **Unit Tests**: Every function has dedicated tests
- **Integration Tests**: End-to-end operation tests
- **Property Tests**: Cryptographic property verification
- **Benchmarks**: Performance measurement and comparison
- **Edge Cases**: Boundary condition testing

### Code Quality
- **Documentation**: Comprehensive comments matching C reference
- **Type Safety**: Strong typing throughout
- **Error Handling**: Proper error propagation
- **Memory Safety**: Secure memory clearing
- **Constant-Time**: Where required for security

---

## Current Status Summary

### Phase 1: ✅ 100% Complete
- Field arithmetic: ✅ 100%
- Scalar arithmetic: ✅ 100%
- Context management: ✅ 100%
- Group operations: ✅ 100% (optimized Jacobian addition complete)
- Public key operations: ✅ 100%

### Phase 2: ✅ 100% Complete
- Hash functions: ✅ 100%
- ECDSA signatures: ✅ 100%
- Private key operations: ✅ 100%
- Key pair generation: ✅ 100%

### Phase 3: ✅ 100% Complete
- ECDH operations: ✅ 100%
- Point multiplication: ✅ 100%
- HKDF key derivation: ✅ 100%

### Phase 4: ✅ 100% Complete
- Schnorr signatures: ✅ 100%
- X-only public keys: ✅ 100%
- Keypair operations: ✅ 100%

---

## Next Steps

### Immediate (Phase 1 Completion)
✅ Phase 1 is complete! All tests passing.

### Short-term (Phase 2)
✅ Phase 2 is complete! All tests passing.

### Medium-term (Phase 3)
✅ Phase 3 is complete! All tests passing.

### Long-term (Phase 4)
✅ Phase 4 is complete! All tests passing.

---

## Files Structure (Complete)

```
p256k1.mleku.dev/
├── go.mod, go.sum
├── Phase 1 (Complete)
│   ├── context.go, context_test.go
│   ├── field.go, field_mul.go, field_test.go
│   ├── scalar.go, scalar_test.go
│   ├── group.go, group_test.go
│   ├── pubkey.go, pubkey_test.go
│   └── ecmult_gen.go
├── Phase 2 (Complete)
│   ├── hash.go, hash_test.go
│   ├── ecdsa.go, ecdsa_test.go
│   ├── eckey.go, eckey_test.go
│   ├── ecdsa_bench_test.go
│   └── BENCHMARK_RESULTS.md
├── Phase 3 (Complete)
│   ├── ecdh.go, ecdh_test.go
│   └── (ecmult functions included in ecdh.go)
└── Phase 4 (Complete)
    ├── schnorr.go, schnorr_test.go
    └── extrakeys.go, extrakeys_test.go
```

---

**Last Updated**: Phase 4 implementation complete, 100% test success. All four phases complete! Schnorr signatures, X-only public keys, and keypair operations all working.
**Target**: Complete port of secp256k1 C library to Go with full feature parity