# Security Audit Guide for clock-bigint

This document provides guidance for security auditors reviewing the clock-bigint library.

## Overview

clock-bigint is a constant-time big integer library for blockchain consensus engines. It implements cryptographic arithmetic with a focus on timing attack resistance and mathematical correctness.

## Architecture Overview

### Core Components

1. **Big Integer Types** (`types.rs`):
   - `BigInt`: Dynamic-length arbitrary precision integers
   - `BigIntFixed<L>`: Fixed-length integers (U256, U512, U1024, U2048)

2. **Arithmetic Operations**:
   - Addition/Subtraction (`add.rs`, `sub.rs`)
   - Multiplication (`mul.rs`)
   - Division/Remainder (`div.rs`)
   - Modular Exponentiation (`modexp.rs`)

3. **Montgomery Arithmetic** (`montgomery.rs`):
   - Montgomery reduction and multiplication
   - Critical for constant-time modular arithmetic

4. **Encoding** (`encode.rs`):
   - Canonical encoding/decoding
   - Deterministic representation

### Security-Critical Properties

1. **Constant-time execution**: All operations must execute in constant time
2. **Mathematical correctness**: All operations must produce correct results
3. **Memory safety**: No buffer overflows or memory corruption
4. **Canonical representation**: Unique encoding for each integer value

## Audit Checklist

### 1. Constant-Time Verification

#### Code Review Points
- [ ] All loops have fixed iteration counts based on type parameters
- [ ] No early returns based on secret data
- [ ] No secret-dependent memory access patterns
- [ ] All conditional operations are branch-free (use CMOV/select)
- [ ] Montgomery context precomputation doesn't leak timing

#### Critical Functions to Review
```rust
// In montgomery.rs
pub fn mont_mul(ctx: &MontgomeryContext, a: &BigInt, b: &BigInt) -> Result<BigInt>

// In modexp.rs
pub fn mod_pow(ctx: &MontgomeryContext, base: &BigInt, exponent: &BigInt) -> Result<BigInt>

// In mul.rs
fn comba_mul(a: &[Limb], b: &[Limb], c: &mut [Limb])
fn karatsuba_mul(a: &[Limb], b: &[Limb], c: &mut [Limb])
```

#### Testing
- [ ] Run constant-time fuzz target: `cargo fuzz run constant_time`
- [ ] Verify timing test results don't show significant variance
- [ ] Check that operations with different secret inputs have similar timing

### 2. Mathematical Correctness

#### Algorithm Verification
- [ ] Montgomery reduction produces correct results
- [ ] Modular exponentiation follows Montgomery ladder algorithm
- [ ] Karatsuba multiplication is correctly implemented
- [ ] Division algorithm handles all edge cases

#### Test Coverage
- [ ] Run full test suite: `cargo test`
- [ ] Verify property-based tests: `cargo test --test compliance`
- [ ] Check fuzz testing covers edge cases
- [ ] Validate against known good implementations (GMP, OpenSSL)

#### Edge Cases
- [ ] Zero operands
- [ ] Maximum value operands
- [ ] Carry propagation across all limbs
- [ ] Division by small/large divisors

### 3. Memory Safety

#### Bounds Checking
- [ ] All array accesses are bounds-checked
- [ ] Limb arithmetic doesn't overflow
- [ ] Dynamic BigInt respects maximum limb limits

#### Memory Management
- [ ] No uninitialized memory usage
- [ ] Proper cleanup of sensitive data (if applicable)
- [ ] No memory leaks in error paths

### 4. Implementation Quality

#### Code Quality
- [ ] No unsafe code in security-critical paths
- [ ] Clear documentation for all public APIs
- [ ] Comprehensive error handling
- [ ] No debug assertions in release builds

#### Performance
- [ ] Benchmark results meet performance targets
- [ ] No performance regressions
- [ ] Gas costs are precomputable and accurate

## Testing Methodology

### Unit Tests
```bash
cargo test --lib
```

### Integration Tests
```bash
cargo test --test integration
```

### Property-Based Testing
```bash
cargo test --test compliance
```

### Fuzz Testing
```bash
# Constant-time verification
cargo fuzz run constant_time

# Edge case discovery
cargo fuzz run edge_cases

# Cryptographic operations
cargo fuzz run crypto_ops
```

### Benchmarks
```bash
cargo bench
```

## Security Test Results

### Expected Results

1. **Timing Analysis**: All operations should show consistent timing regardless of input values
2. **Mathematical Verification**: All test vectors should pass
3. **Memory Safety**: No crashes, leaks, or undefined behavior
4. **Performance**: Meet or exceed performance targets

### Failure Criteria

1. **Timing Leaks**: >5% timing variation between different secret inputs
2. **Mathematical Errors**: Any incorrect computation results
3. **Memory Corruption**: Any crashes or undefined behavior
4. **Performance Regression**: >10% slowdown from baseline

## Known Limitations

1. **Trust in Compiler**: Assumes Rust compiler preserves constant-time properties
2. **Hardware Assumptions**: No protection against microarchitectural attacks
3. **Dependency Trust**: Relies on audited dependencies
4. **Formal Verification**: Some algorithms lack formal proofs

## Recommendations

### For Auditors
1. Focus on constant-time properties in critical functions
2. Verify mathematical correctness through testing
3. Check for side channel leakage in new code
4. Ensure comprehensive test coverage

### For Developers
1. Maintain constant-time properties in all modifications
2. Add tests for new functionality
3. Update benchmarks when making performance changes
4. Run security tests before releases

## Contact Information

For security issues, please contact the maintainers through the repository's security advisory process.

## Version Information

- **Version**: 0.1.0
- **Specification**: ClockinChain Big Integer Specification v1.0
- **Last Audit**: [Date]
- **Next Audit**: [Date]