Post-Quantum Signature

🦅 Falcon-512 Compact Lattice Signatures

Security Level 128-bit post-quantum
Performance ⭐⭐⭐⭐ Very Good
Quantum Resistant ✅ Yes
Signature Size ~690 bytes (compact!)
Public Key 897 bytes
Private Key 1281 bytes

📋 Quick Navigation

📖 Overview 🔧 Algorithm Details 💻 Implementation 🔒 Security ⚡ Performance ⚖️ Comparison

📖 Overview

Falcon-512 is a lattice-based digital signature algorithm that offers the most compact signatures among NIST post-quantum candidates. Built on NTRU lattices with fast Fourier sampling, it provides excellent security with minimal bandwidth requirements.

✨ Key Features

📏

Ultra-Compact Signatures

Smallest signatures among NIST PQC candidates

⚡

Fast Verification

Very efficient signature verification process

🔢

NTRU-Based

Built on well-studied NTRU lattice problems

🛡️

Quantum-Resistant

Secure against both classical and quantum attacks

📶

Bandwidth Efficient

Ideal for constrained network environments

🔬

FFT Sampling

Uses fast Fourier sampling for efficiency

🎯 Common Use Cases

🌐 Bandwidth-Limited Applications

  • IoT device authentication with limited connectivity
  • Satellite communications with high latency
  • Mobile applications with data constraints
  • Embedded systems with minimal storage

🔐 Security-Critical Systems

  • Government and military communications
  • Financial transaction signing
  • Digital certificates and PKI
  • Code signing for software distribution

🔧 Algorithm Details

📊 Falcon-512 Specifications

Security Level
NIST Level 1
128-bit post-quantum security
Public Key
897 bytes
Compressed public key size
Private Key
1281 bytes
Secret key storage requirement
Signature Size
~690 bytes
Variable, most compact PQ signature

🔐 Security Properties

🔢

NTRU Assumption

Based on well-studied lattice problems

⚡

Fast Verification

Efficient signature verification process

🎯

Low Failure Rate

Negligible signature generation failures

🛡️

Strong Unforgeability

EUF-CMA security against quantum attacks

🧮 Algorithm Structure

Falcon uses the GPV framework over NTRU lattices:

Signature = FFT_Sample(lattice, target, σ)

Where σ is the Gaussian parameter and FFT sampling ensures compact signatures.

💻 Implementation

Falcon-512 is optimized for applications requiring minimal signature sizes. The variable signature length averages around 690 bytes, making it ideal for bandwidth-constrained environments.

Basic Signing and Verification

Falcon-512 Compact Signatures Python
```python from metamui_crypto import Falcon512 # Key Generation keypair = Falcon512.generate_keypair() # Sign a message message = b"Compact signature demonstration" signature = Falcon512.sign(message, keypair.private_key) # Verify the signature is_valid = Falcon512.verify(signature, message, keypair.public_key) print(f"Signature valid: {is_valid}") print(f"Public key size: {len(keypair.public_key)} bytes") print(f"Private key size: {len(keypair.private_key)} bytes") print(f"Signature size: {len(signature)} bytes") # Demonstrate compactness print(f"Signature is {len(signature)} bytes - most compact among PQ algorithms!") ```

🔒 Security Considerations

⚠️ Important Security Guidelines

  • Monitor signature generation for rare failure cases
  • Use secure random number generation for key generation
  • Implement proper key storage for larger private keys
  • Consider hybrid signatures for transition periods
  • Validate public keys before signature verification

⚡ Performance Analysis

Signature Size Comparison

Algorithm Signature Size Public Key Size Quantum Safe
Falcon-512 ~690 bytes 897 bytes ✅ Yes
Dilithium2 2420 bytes 1312 bytes ✅ Yes
Dilithium3 3293 bytes 1952 bytes ✅ Yes
Ed25519 64 bytes 32 bytes ❌ No
RSA-2048 256 bytes 256 bytes ❌ No

⚖️ Comparison with Other Post-Quantum Signatures

Falcon vs Dilithium vs Classical

Aspect Falcon-512 Dilithium3 Ed25519
Signature Size ~690 bytes 3293 bytes 64 bytes
Speed (Sign) Medium Fast Very Fast
Speed (Verify) Fast Fast Fast
Key Generation Slow Fast Very Fast
Bandwidth Use Best PQ Higher Excellent
Quantum Safe Yes Yes No

📚 References

Other Post-Quantum Signatures

🔐

Dilithium

NIST standardized ML-DSA
✍️

Ed25519

Classical elliptic curve signatures
🔑

ML-KEM-768

Post-quantum key encapsulation

 
from metamui_crypto import Falcon512
import statistics

# Falcon signatures have variable size
keypair = Falcon512.generate_keypair()
messages = [f"Message {i}".encode() for i in range(100)]

# Sign multiple messages
signatures = [Falcon512.sign(msg, keypair.private_key) for msg in messages]

# Analyze signature sizes
sizes = [len(sig) for sig in signatures]
print(f"Average size: {statistics.mean(sizes):.1f} bytes")
print(f"Min size: {min(sizes)} bytes")
print(f"Max size: {max(sizes)} bytes")

Serialization with Compression

from metamui_crypto import Falcon512
import zlib
import base64

# Generate keypair
keypair = Falcon512.generate_keypair()

# Serialize public key (fixed size)
public_key_bytes = keypair.public_key.to_bytes()

# Sign and compress signature
message = b"Important document"
signature = Falcon512.sign(message, keypair.private_key)

# Optional: Compress for storage/transmission
compressed_sig = zlib.compress(signature)
encoded_sig = base64.b64encode(compressed_sig).decode()

print(f"Original signature: {len(signature)} bytes")
print(f"Compressed: {len(compressed_sig)} bytes")

Batch Signing with Size Optimization

from metamui_crypto import Falcon512

class BatchSigner:
    def __init__(self, private_key):
        self.private_key = private_key
    
    def sign_batch(self, messages, max_attempts=3):
        """Sign messages, retry for smaller signatures"""
        signatures = []
        
        for message in messages:
            best_sig = None
            best_size = float('inf')
            
            # Try multiple times to get smaller signature
            for _ in range(max_attempts):
                sig = Falcon512.sign(message, self.private_key)
                if len(sig) < best_size:
                    best_sig = sig
                    best_size = len(sig)
            
            signatures.append(best_sig)
        
        return signatures

Implementation Details

Core Components

  1. NTRU Lattices
    • Polynomial ring: Z[X]/(X^512 + 1)
    • Efficient polynomial arithmetic
    • Compact key representation
  2. Fast Fourier Sampling
    • Uses FFT for Gaussian sampling
    • Enables small signatures
    • Complex but efficient algorithm
  3. Floating-Point Arithmetic
    • Requires high precision
    • Careful implementation needed
    • Platform-specific optimizations
  4. Tree-Based Signing
    • Binary tree structure
    • Recursive signature generation
    • Variable signature size

Security Features

  • Strong Unforgeability: Secure against existential forgery
  • Side-Channel Considerations: Floating-point operations need care
  • Randomized Signing: Each signature is unique
  • No Signature Compression: Already optimally small

Performance Characteristics

Speed Benchmarks

Operation Time Notes
Key Generation 8.5 ms One-time operation
Sign 1.5 ms Variable by message
Verify 0.3 ms Very fast

Size Comparison

Algorithm Public Key Private Key Signature
Falcon-512 897 bytes 1281 bytes ~690 bytes
Dilithium2 1312 bytes 2528 bytes 2420 bytes
RSA-2048 256 bytes 256 bytes 256 bytes
Ed25519 32 bytes 32 bytes 64 bytes

Advanced Usage

Streaming Signatures

from metamui_crypto import Falcon512
import io

class StreamingSigner:
    def __init__(self, private_key):
        self.private_key = private_key
    
    def sign_stream(self, stream, chunk_size=4096):
        """Sign data from a stream"""
        hasher = Falcon512.new_hasher()
        
        while True:
            chunk = stream.read(chunk_size)
            if not chunk:
                break
            hasher.update(chunk)
        
        # Sign the hash
        digest = hasher.finalize()
        return Falcon512.sign_digest(digest, self.private_key)

Threshold Signatures

from metamui_crypto import Falcon512

class ThresholdFalcon:
    """Simplified threshold signature scheme"""
    
    def __init__(self, threshold, total_parties):
        self.threshold = threshold
        self.total_parties = total_parties
        self.shares = self._generate_shares()
    
    def _generate_shares(self):
        # Generate master keypair
        master = Falcon512.generate_keypair()
        
        # Split private key into shares (simplified)
        # In practice, use proper secret sharing
        shares = []
        for i in range(self.total_parties):
            share_keypair = Falcon512.generate_keypair()
            shares.append({
                'id': i,
                'keypair': share_keypair,
                'master_public': master.public_key
            })
        
        return shares
    
    def partial_sign(self, message, share_id):
        """Create partial signature"""
        share = self.shares[share_id]
        return Falcon512.sign(message, share['keypair'].private_key)
    
    def combine_signatures(self, partial_sigs, message):
        """Combine threshold signatures (simplified)"""
        if len(partial_sigs) < self.threshold:
            raise ValueError("Insufficient signatures")
        
        # In practice, use proper combination algorithm
        # This is a simplified demonstration
        return partial_sigs[0]  # Use first valid signature

Integration Guide

Bandwidth-Constrained Systems

from metamui_crypto import Falcon512, ChaCha20Poly1305

class CompactProtocol:
    """Protocol optimized for minimal bandwidth"""
    
    def __init__(self):
        self.signing_key = Falcon512.generate_keypair()
        self.encryption_key = os.urandom(32)
    
    def create_packet(self, data):
        # Encrypt data
        nonce = os.urandom(12)
        cipher = ChaCha20Poly1305(self.encryption_key)
        ciphertext, tag = cipher.encrypt(data, nonce)
        
        # Sign the ciphertext
        signature = Falcon512.sign(
            nonce + ciphertext + tag,
            self.signing_key.private_key
        )
        
        # Total overhead: ~690 bytes (signature) + 12 (nonce) + 16 (tag)
        return {
            'nonce': nonce,
            'ciphertext': ciphertext,
            'tag': tag,
            'signature': signature
        }

IoT Device Implementation

from metamui_crypto import Falcon512
import struct
import time

class IoTDevice:
    def __init__(self, device_id):
        self.device_id = device_id
        self.keypair = Falcon512.generate_keypair()
        self.message_counter = 0
    
    def create_telemetry_message(self, sensor_data):
        # Create compact message
        timestamp = int(time.time())
        
        # Pack data efficiently
        message = struct.pack(
            '<I I H f f',  # Little-endian: device_id, timestamp, counter, temp, humidity
            self.device_id,
            timestamp,
            self.message_counter,
            sensor_data['temperature'],
            sensor_data['humidity']
        )
        
        # Sign the message
        signature = Falcon512.sign(message, self.keypair.private_key)
        
        self.message_counter += 1
        
        # Total size: 18 bytes (message) + ~690 bytes (signature)
        return message + signature

Common Pitfalls

1. Assuming Fixed Signature Size

# Bad: Assuming fixed size
# buffer = bytearray(690)  # May be too small!

# Good: Handle variable size
signature = Falcon512.sign(message, private_key)
buffer = bytearray(len(signature))

2. Floating-Point Determinism

# Falcon uses floating-point internally
# Results may vary slightly across platforms

# Good: Test on target platform
def test_platform_compatibility():
    keypair = Falcon512.generate_keypair()
    message = b"test"
    
    signatures = []
    for _ in range(10):
        sig = Falcon512.sign(message, keypair.private_key)
        signatures.append(sig)
    
    # All should verify
    for sig in signatures:
        assert Falcon512.verify(sig, message, keypair.public_key)

3. Key Generation Performance

# Bad: Generating keys frequently
# for message in messages:
#     keypair = Falcon512.generate_keypair()  # Slow!
#     signature = Falcon512.sign(message, keypair.private_key)

# Good: Reuse keypair
keypair = Falcon512.generate_keypair()  # Once
for message in messages:
    signature = Falcon512.sign(message, keypair.private_key)

Performance Optimization

Platform-Specific Optimizations

from metamui_crypto import Falcon512
import platform

class OptimizedFalcon:
    def __init__(self):
        self.system = platform.system()
        self.arch = platform.machine()
        
        # Use optimized implementation if available
        if self.arch in ['x86_64', 'amd64']:
            # AVX2 optimizations available
            self.impl = Falcon512.get_avx2_implementation()
        elif self.arch.startswith('arm'):
            # NEON optimizations
            self.impl = Falcon512.get_neon_implementation()
        else:
            # Fallback to portable
            self.impl = Falcon512.get_portable_implementation()
    
    def sign(self, message, private_key):
        return self.impl.sign(message, private_key)

Memory-Efficient Batch Processing

def process_large_dataset(filename, private_key, chunk_size=1000):
    """Process large file with minimal memory usage"""
    
    with open(filename, 'rb') as f:
        while True:
            # Read chunk of messages
            messages = []
            for _ in range(chunk_size):
                length_bytes = f.read(4)
                if not length_bytes:
                    break
                
                length = struct.unpack('<I', length_bytes)[0]
                message = f.read(length)
                messages.append(message)
            
            if not messages:
                break
            
            # Process chunk
            for message in messages:
                signature = Falcon512.sign(message, private_key)
                yield message, signature

Migration Considerations

From RSA/ECDSA

# Size comparison for migration planning
def analyze_signature_overhead():
    # Current RSA-2048
    rsa_signature_size = 256
    
    # Falcon-512 average
    falcon_avg_size = 690
    
    # For 1 million signatures
    rsa_total = rsa_signature_size * 1_000_000
    falcon_total = falcon_avg_size * 1_000_000
    
    print(f"RSA-2048: {rsa_total / 1_000_000:.1f} MB")
    print(f"Falcon-512: {falcon_total / 1_000_000:.1f} MB")
    print(f"Increase: {(falcon_total - rsa_total) / rsa_total * 100:.1f}%")

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