DJB Algorithms in MetaMUI

Technical details of Daniel J. Bernstein’s algorithms implemented in MetaMUI

This section provides comprehensive technical documentation for DJB’s algorithms as implemented in MetaMUI, highlighting their innovative design principles and performance characteristics.

Core DJB Algorithm Family

ChaCha20: Software-Optimized Stream Cipher

Design Innovation

ARX (Add-Rotate-XOR) construction for universal software performance

ChaCha20 Quarter Round:
a += b; d ^= a; d <<<= 16;
c += d; b ^= c; b <<<= 12;  
a += b; d ^= a; d <<<= 8;
c += d; b ^= c; b <<<= 7;

Technical Specifications

  • Key Size: 256 bits (32 bytes)
  • Nonce Size: 96 bits (12 bytes)
  • Block Size: 512 bits (64 bytes)
  • Security Level: 256-bit classical, ~128-bit post-quantum
  • Performance: ~1,200 MB/s on modern CPUs (software-only)

DJB’s Design Philosophy Realized

  • Software First: No lookup tables, only simple arithmetic operations
  • Constant Time: All operations complete in fixed time regardless of input
  • Universal Performance: Consistent speed across all CPU architectures
  • Simple Structure: 20 rounds of identical quarter-round operations

MetaMUI Implementation Highlights

def chacha20_encrypt(plaintext, key, nonce, counter=0):
    """
    ChaCha20 encryption following DJB's exact specification
    - Pure software implementation
    - Constant-time operations
    - No data-dependent branching
    """
    state = chacha20_initial_state(key, nonce, counter)
    keystream = chacha20_block(state)
    return xor_bytes(plaintext, keystream)

Poly1305: Elegant Message Authentication

Mathematical Foundation

Prime field arithmetic for speed and security

Poly1305 MAC computation:
h = ((h + m) * r) mod (2^130 - 5)

Technical Specifications

  • Key Size: 256 bits (32 bytes) - used once per message
  • Tag Size: 128 bits (16 bytes)
  • Security: Information-theoretic with proper key usage
  • Performance: Single-pass computation, ~1,500 MB/s

DJB’s Innovation

  • One-Time Keys: Each message uses unique key derived from master key
  • Prime Field: Arithmetic modulo 2^130 - 5 for efficient computation
  • Carry-less: Minimal carry propagation for consistent timing
  • Elegant Math: Beautiful mathematical structure enabling fast implementation

MetaMUI Integration

def poly1305_authenticate(message, key):
    """
    Poly1305 one-time authenticator
    - Information-theoretic security
    - Constant-time implementation
    - Single-pass message processing
    """
    r, s = poly1305_key_split(key)
    accumulator = 0
    
    for block in message_blocks(message):
        accumulator = ((accumulator + block) * r) % POLY1305_PRIME
    
    return (accumulator + s) & 0xffffffffffffffffffffffffffffffff

ChaCha20-Poly1305: AEAD Perfection

Architectural Excellence

The apex of DJB’s AEAD design philosophy

ChaCha20-Poly1305 AEAD Construction:
1. Derive Poly1305 key from ChaCha20 keystream
2. Encrypt plaintext with ChaCha20
3. Authenticate ciphertext + AAD with Poly1305
4. Return ciphertext + authentication tag

Technical Specifications

  • Key Size: 256 bits (32 bytes)
  • Nonce Size: 96 bits (12 bytes)
  • Tag Size: 128 bits (16 bytes)
  • Performance: ~1,200 MB/s combined encrypt+authenticate
  • Security: 256-bit keys provide ~128-bit post-quantum security

DJB’s AEAD Vision Realized

  • Single Operation: Combined encryption and authentication
  • Provable Security: Formal security proofs for construction
  • Implementation Safety: Hard to use incorrectly
  • Universal Deployment: No hardware dependencies

MetaMUI Production Implementation

def chacha20_poly1305_encrypt(plaintext, aad, key, nonce):
    """
    ChaCha20-Poly1305 AEAD encryption
    - Derive Poly1305 key from first ChaCha20 block
    - Encrypt plaintext with ChaCha20 starting from counter=1
    - Authenticate AAD + ciphertext with Poly1305
    """
    # Derive one-time Poly1305 key
    poly_key = chacha20_block(key, nonce, counter=0)[:32]
    
    # Encrypt plaintext
    ciphertext = chacha20_encrypt(plaintext, key, nonce, counter=1)
    
    # Authenticate AAD + ciphertext
    auth_data = aad + ciphertext + encode_lengths(len(aad), len(ciphertext))
    tag = poly1305_authenticate(auth_data, poly_key)
    
    return ciphertext, tag

Elliptic Curve Cryptography Revolution

Curve25519: Montgomery Curve Excellence

Mathematical Innovation

Montgomery curves for fast, secure key exchange

Curve25519 equation: y² = x³ + 486662x² + x
Prime field: p = 2^255 - 19
Base point: x = 9

Technical Specifications

  • Key Size: 256 bits (32 bytes) private, 32 bytes public
  • Security Level: ~128 bits classical, ~64 bits post-quantum
  • Performance: 50,000+ scalar multiplications per second
  • Cofactor: 8 (handled automatically in implementation)

DJB’s Curve Design Principles

  • Montgomery Form: Efficient x-coordinate-only arithmetic
  • Complete Addition: No special cases in point addition
  • Twist Security: Both curve and quadratic twist are secure
  • Constant Time: Fixed execution time regardless of secret values

X25519: Practical Key Exchange

Protocol Simplicity

Diffie-Hellman key exchange perfected

X25519 Key Exchange:
Alice: a (private), A = a·G (public)
Bob:   b (private), B = b·G (public)
Shared: a·B = b·A = ab·G

Technical Implementation

  • Input Clamping: Private keys clamped to valid range
  • Output Format: 32-byte shared secret
  • Side-Channel Resistance: Constant-time scalar multiplication
  • Twist Security: Secure against invalid curve attacks

MetaMUI X25519 Implementation

def x25519_key_exchange(private_key, public_key):
    """
    X25519 Elliptic Curve Diffie-Hellman
    - Constant-time scalar multiplication
    - Automatic input validation and clamping
    - Twist-secure implementation
    """
    # Clamp private key to valid range
    private_clamped = clamp_private_key(private_key)
    
    # Perform scalar multiplication: private * public
    shared_point = curve25519_scalar_mult(private_clamped, public_key)
    
    # Return x-coordinate as shared secret
    return shared_point[:32]

Ed25519: Signature Algorithm Perfection

Edwards Curve Advantages

Complete, fast, and secure digital signatures

Ed25519 curve equation: -x² + y² = 1 + (121665/121666)x²y²
Signature: (R, S) where R = r·G, S = (r + H(R,A,M)·a) mod ℓ

Technical Specifications

  • Key Size: 256 bits (32 bytes) private, 32 bytes public
  • Signature Size: 512 bits (64 bytes)
  • Performance: 8,000+ signatures/sec, 12,000+ verifications/sec
  • Security: 128-bit security level with strong implementation safety

DJB’s Signature Innovation

  • Deterministic: Same message always produces same signature
  • Complete Group Law: No exceptional cases in point arithmetic
  • Batch Verification: Multiple signatures verified together efficiently
  • EdDSA Framework: Generalizable to other Edwards curves

MetaMUI Ed25519 Foundation

def ed25519_sign(message, private_key):
    """
    Ed25519 digital signature
    - Deterministic signature generation
    - Constant-time implementation
    - Complete Edwards curve arithmetic
    """
    # Derive public key and signing nonce
    public_key = ed25519_public_key(private_key)
    r = hash_to_scalar(private_key + message)
    
    # Compute signature components
    R = scalar_mult_base(r)
    h = hash_to_scalar(R + public_key + message)
    S = (r + h * private_key) % CURVE_ORDER
    
    return R + S  # 64-byte signature

DJB-Inspired Extensions in MetaMUI

Sr25519: Blockchain Evolution of Ed25519

Ristretto Group Innovation

Removing cofactor complications from Ed25519

Sr25519 = Ed25519 + Ristretto + Schnorr
- Ristretto eliminates cofactor 8 from Curve25519
- Schnorr signatures enable batch verification
- Blockchain-optimized for consensus algorithms

Technical Enhancements

  • Prime Order Group: Ristretto provides clean prime-order group
  • Batch Verification: Verify multiple signatures simultaneously
  • VRF Capability: Verifiable Random Function extensions
  • Substrate Integration: Native blockchain framework support

Blockchain Performance Optimization

def sr25519_batch_verify(signatures, messages, public_keys):
    """
    Sr25519 batch signature verification
    - Extends Ed25519 with Ristretto encoding
    - Optimized for blockchain consensus
    - Linear scaling with batch size
    """
    # Combine all signatures into single verification equation
    combined_signature = combine_signatures(signatures)
    combined_commitment = combine_commitments(signatures, messages, public_keys)
    
    # Single point verification instead of individual checks
    return verify_combined_equation(combined_signature, combined_commitment)

Blake3: Parallel Hashing Philosophy

DJB Performance Principles Applied

Extreme parallelization following software-first philosophy

Blake3 Features:
- Tree-based parallel processing
- SIMD optimization
- Streaming capability
- Universal performance

Architectural Alignment with DJB

  • Software Optimization: No hardware dependencies
  • Parallel by Design: Utilizes all available CPU cores
  • Simple API: Single function for all use cases
  • Constant Time: Uniform processing regardless of input

MetaMUI Blake3 Integration

def blake3_hash_parallel(data, num_threads=None):
    """
    Blake3 parallel hashing
    - Follows DJB's software-first philosophy
    - Utilizes all available CPU cores
    - Maintains constant-time properties
    """
    if num_threads is None:
        num_threads = cpu_count()
    
    # Divide input across threads for parallel processing
    chunks = divide_data(data, num_threads)
    
    # Hash chunks in parallel
    chunk_hashes = parallel_map(blake3_hash_chunk, chunks)
    
    # Combine chunk hashes into final result
    return blake3_combine_tree(chunk_hashes)

Algorithm Performance Characteristics

Software Optimization Metrics

ChaCha20 Performance Analysis

Platform Performance (MB/s):
├── x86_64 (AVX2): 1,500 MB/s
├── ARM64 (NEON): 1,200 MB/s  
├── ARM32: 400 MB/s
├── RISC-V: 300 MB/s
└── WebAssembly: 200 MB/s

Consistent Performance Ratio: 7.5:1 (best:worst)
Compare to AES: 15:1 ratio (hardware dependent)

X25519 Operations per Second

Key Exchange Performance:
├── Key Generation: 25,000 ops/sec
├── Public Key Derivation: 50,000 ops/sec
├── Shared Secret: 50,000 ops/sec
└── Memory Usage: 64 bytes per operation

Advantage over RSA-2048: 100x faster
Advantage over ECDH P-256: 2.5x faster

Ed25519 Signature Performance

Digital Signature Performance:
├── Sign: 8,000 ops/sec
├── Verify: 12,000 ops/sec
├── Batch Verify (100): 50,000 ops/sec
└── Memory Usage: 96 bytes per operation

Advantage over RSA-2048: 200x faster signing
Advantage over ECDSA P-256: 3x faster overall

Memory Efficiency Comparison

State Size Analysis

Algorithm Memory Requirements:
├── ChaCha20: 64 bytes state
├── Poly1305: 32 bytes accumulator
├── X25519: 32 bytes intermediate
├── Ed25519: 64 bytes signature buffer
└── Combined AEAD: <200 bytes total

Traditional Comparison:
├── AES-GCM: 300+ bytes (with tables)
├── RSA-2048: 2,048+ bytes
├── ECDSA P-256: 256+ bytes
└── SHA-256: 64 bytes

Security Properties and Analysis

Cryptanalytic Resistance

ChaCha20 Security Margins

  • Rounds: 20 rounds (8 rounds broken, 12+ margin)
  • Key Recovery: No attacks better than brute force
  • Distinguishers: No practical distinguishing attacks
  • Side Channels: Constant-time implementation resists timing attacks

Curve25519 Security Assessment

  • Discrete Log: Best attacks require ~2^125 operations
  • Invalid Curve: Twist-secure against invalid point attacks
  • Small Subgroup: Cofactor handled transparently
  • Quantum Resistance: ~64-bit security against Shor’s algorithm

Ed25519 Signature Security

  • Forgery Resistance: No known forgery attacks
  • Key Recovery: Requires discrete logarithm solution
  • Malleability: Non-malleable signatures
  • Batch Verification: Maintains security in batch mode

Implementation Security Features

Constant-Time Guarantees

# All DJB algorithms implement constant-time operations
def constant_time_example():
    """
    DJB algorithms avoid:
    - Data-dependent branching
    - Data-dependent memory access
    - Variable-time arithmetic
    - Secret-dependent loop counts
    """
    # Instead use:
    # - Branchless conditional moves
    # - Uniform memory access patterns  
    # - Fixed-time arithmetic
    # - Constant iteration counts

Side-Channel Resistance

  • Timing Attacks: Fixed execution time regardless of inputs
  • Cache Attacks: Uniform memory access patterns
  • Power Analysis: Uniform power consumption profiles
  • Electromagnetic: Consistent EM signature patterns

Integration with Modern Cryptography

Post-Quantum Coexistence

Symmetric Algorithms (Unchanged)

  • ChaCha20-Poly1305: Maintains full security in PQC era
  • Blake3: Hash function security unaffected by quantum computers
  • Key Sizes: 256-bit keys provide ~128-bit post-quantum security

Asymmetric Algorithm Evolution

  • X25519 → ML-KEM-768: Key exchange evolution path
  • Ed25519 → Falcon-512: Signature algorithm progression
  • Hybrid Modes: Classical+PQC for defense-in-depth

MetaMUI’s DJB Legacy Continuation

Principles Maintained

  • Software First: PQC algorithms also software-optimized
  • Simple APIs: Same ease-of-use philosophy maintained
  • Constant Time: PQC implementations follow timing-safe patterns
  • Universal Performance: Consistent behavior across platforms

Innovation Continues

  • Parallel Processing: Blake3 extends DJB performance philosophy
  • Blockchain Focus: Sr25519 adapts Ed25519 for distributed systems
  • Mobile Optimization: Falcon-512 continues mobile-first approach
  • Standards Compliance: ML-KEM-768 balances innovation with standardization