X25519 Protocol

The X25519 protocol implementation provides standard Curve25519-based Diffie-Hellman key exchange for secure key agreement.

Overview

The X25519 protocol uses Curve25519 and provides:

• X25519 Diffie-Hellman key agreement

• AES-256-GCM key wrapping

• Standard compliance with RFC 7748

• High performance key exchange

Cryptographic Primitives

Curve Parameters

• Curve: Curve25519 (y² = x³ + 486662x² + x)

• Field: Prime field with characteristic 2²⁵⁵ - 19

• Base point: u = 9

• Order: Prime order ≈ 2²⁵²

Key Sizes

• Private Key: 32 bytes (scalar)

• Public Key: 32 bytes (u-coordinate)

• Ephemeral Public Key: 32 bytes (u-coordinate)

• Shared Secret: 32 bytes (u-coordinate)

Key Features

1. Standard X25519 Key Exchange

The X25519 protocol implements the standard Diffie-Hellman key exchange:

use privacy_engine::chains::x25519::X25519Protocol;

let protocol = X25519Protocol::new();

// Generate key pair
let (private_key, public_key) = protocol.generate_keypair()?;

// Perform key agreement
let (ephemeral_secret, ephemeral_pubkey) = protocol.generate_ephemeral_keypair()?;
let shared_secret = protocol.derive_shared_secret(&ephemeral_secret, &recipient_pubkey)?;

2. High-Performance Key Agreement

X25519 is optimized for performance:

• Fast scalar multiplication using Montgomery curves

• Constant-time operations for side-channel resistance

• Efficient key derivation without additional hashing

3. Standard Compliance

The implementation follows RFC 7748 standards:

• Clamping: Private keys are properly clamped

• Coordinate validation: Public keys are validated

• Error handling: Proper error handling for invalid inputs

Implementation Details

Key Generation

// Generate private key (32 bytes)
let mut private_key = [0u8; 32];
OsRng.fill_bytes(&mut private_key);

// Generate public key
let public_key = x25519(private_key, X25519_BASEPOINT_BYTES);

Key Agreement

// Generate ephemeral key pair
let ephemeral_secret = EphemeralSecret::random_from_rng(&mut OsRng);
let ephemeral_pubkey = PublicKey::from(&ephemeral_secret);

// Perform X25519 key agreement
let recipient_pubkey = PublicKey::from(recipient_pubkey_bytes);
let shared_secret = ephemeral_secret.diffie_hellman(&recipient_pubkey);

// Use shared secret directly as AES key
let aes_key = Key::<Aes256Gcm>::from_slice(shared_secret.as_bytes());

Key Wrapping

// Encrypt symmetric key with X25519
let cipher = Aes256Gcm::new(aes_key);
let mut nonce_bytes = [0u8; 12];
OsRng.fill_bytes(&mut nonce_bytes);
let nonce = Nonce::from_slice(&nonce_bytes);

let ciphertext = cipher.encrypt(nonce, symmetric_key)?;

Ok(EncryptedData {
    ciphertext,
    nonce: nonce_bytes.to_vec(),
    ephemeral_pubkey: ephemeral_pubkey.as_bytes().to_vec(),
})

Usage Examples

Basic Key Encryption

use privacy_engine::chains::x25519::X25519Protocol;
use privacy_engine::types::{EncryptedData, CryptoError};

let protocol = X25519Protocol::new();
let recipient_pubkey: Vec<u8> = /* recipient's public key */;
let symmetric_key: Vec<u8> = /* 32-byte symmetric key */;

let encrypted: EncryptedData = protocol.encrypt_key(
    &recipient_pubkey,
    None, // X25519 doesn't use message hash
    &symmetric_key
)?;

Key Decryption

let recipient_private_key: Vec<u8> = /* recipient's private key */;
let decrypted_key: Vec<u8> = protocol.decrypt_key(&encrypted, &recipient_private_key)?;

Key Pair Generation

let protocol = X25519Protocol::new();
let (private_key, public_key) = protocol.generate_keypair()?;

println!("Private key: {:?}", hex::encode(&private_key));
println!("Public key:  {:?}", hex::encode(&public_key));

Ephemeral Key Generation

let protocol = X25519Protocol::new();
let (ephemeral_secret, ephemeral_pubkey) = protocol.generate_ephemeral_keypair()?;

println!("Ephemeral public key: {:?}", hex::encode(&ephemeral_pubkey));

Data Formats

Public Key Format

// 32-byte u-coordinate as little-endian bytes
let public_key: Vec<u8> = vec![0x12, 0x34, /* ... 30 more bytes */];

Private Key Format

// 32-byte scalar as little-endian bytes (clamped)
let private_key: Vec<u8> = vec![0xab, 0xcd, /* ... 30 more bytes */];

Ephemeral Public Key Format

// 32-byte u-coordinate as little-endian bytes
let ephemeral_pubkey: Vec<u8> = vec![0x12, 0x34, /* ... 30 more bytes */];

Shared Secret Format

// 32-byte u-coordinate as little-endian bytes
let shared_secret: Vec<u8> = vec![0x56, 0x78, /* ... 30 more bytes */];

Security Considerations

Key Management

• Private Keys: Never share or log private keys

• Key Generation: Use cryptographically secure random number generation

• Key Storage: Store keys securely using appropriate key management systems

Curve25519 Security

• Clamping: Private keys are automatically clamped for security

• Validation: Public keys are validated before use

• Constant-time: Operations are constant-time to prevent timing attacks

Key Agreement Security

• Ephemeral Keys: Fresh ephemeral keys for each encryption

• No Key Reuse: Shared secrets are never reused

• Forward Secrecy: Each encryption provides forward secrecy

Performance Characteristics

Timing Benchmarks

Operation	Average Time	Notes
Key Generation	~1ms	Fast scalar multiplication
Key Agreement	~2ms	X25519 computation
Key Wrapping	~1ms	AES-256-GCM encryption
Key Unwrapping	~1ms	AES-256-GCM decryption

Memory Usage

• Key Storage: 32 bytes per key

• Ephemeral Keys: 32 bytes per encryption

• Shared Secrets: 32 bytes

• Total Overhead: Minimal compared to other protocols

Performance Comparison

Protocol	Key Generation	Key Agreement	Memory Usage
X25519	~1ms	~2ms	Low
Starknet	~2ms	~3ms	Medium
RSA-2048	~50ms	~100ms	High

Standard Compliance

RFC 7748 Compliance

The implementation follows RFC 7748 "Elliptic Curves for Security":

• Curve25519: Uses the standard Curve25519 curve

• X25519: Implements X25519 key agreement function

• Clamping: Private keys are properly clamped

• Validation: Public keys are validated according to the standard

Interoperability

The implementation is compatible with:

• OpenSSL: X25519 implementation

• libsodium: Curve25519 implementation

• Bouncy Castle: Java implementation

• Other RFC 7748 compliant libraries

Testing

Unit Tests

# Run X25519-specific tests
cargo test --test x25519_protocol

# Run with verbose output
cargo test --test x25519_protocol -- --nocapture

Integration Tests

# Test X25519 key exchange
cargo test --test x25519_integration -- --nocapture

Interoperability Tests

# Test compatibility with other implementations
cargo test --test x25519_interop -- --nocapture

Error Handling

Common Errors

#[derive(Error, Debug)]
pub enum CryptoError {
    #[error("Invalid key length (expected 32)")]
    InvalidKeyLength,
    #[error("Invalid public key")]
    InvalidPublicKey,
    #[error("Encryption failed")]
    EncryptionError(String),
    #[error("Decryption failed")]
    DecryptionError(String),
    // ... other errors
}

Error Recovery

match protocol.encrypt_key(&pubkey, None, &key) {
    Ok(encrypted) => {
        // Success
    }
    Err(CryptoError::InvalidKeyLength) => {
        // Invalid key size
    }
    Err(CryptoError::InvalidPublicKey) => {
        // Invalid public key format
    }
    Err(CryptoError::EncryptionError(msg)) => {
        // Encryption failed
    }
    Err(e) => {
        // Other errors
    }
}

Best Practices

Key Generation

// Use secure random number generation
let mut private_key = [0u8; 32];
OsRng.fill_bytes(&mut private_key);

// Keys are automatically clamped
let public_key = x25519(private_key, X25519_BASEPOINT_BYTES);

Key Validation

// Validate public key before use
let public_key: [u8; 32] = recipient_pubkey.try_into()
    .map_err(|_| CryptoError::InvalidKeyLength)?;

// X25519 will validate the key internally
let shared_secret = ephemeral_secret.diffie_hellman(&PublicKey::from(public_key));

Performance Optimization

// Reuse protocol instance for multiple operations
let protocol = X25519Protocol::new();

for recipient in recipients {
    let encrypted = protocol.encrypt_key(&recipient.pubkey, None, &key)?;
    // Process encrypted key
}

Integration Examples

Web Application

// Example: Encrypting session keys for web clients
let protocol = X25519Protocol::new();
let client_pubkey = /* from client */;
let session_key = /* generated session key */;

let encrypted_session = protocol.encrypt_key(&client_pubkey, None, &session_key)?;

// Send encrypted session key to client
send_to_client(encrypted_session);

IoT Device Communication

// Example: Secure communication between IoT devices
let protocol = X25519Protocol::new();

// Device A encrypts message for Device B
let device_b_pubkey = /* Device B's public key */;
let message = /* sensor data */;

let encrypted = protocol.encrypt_key(&device_b_pubkey, None, &message)?;

// Device B decrypts using its private key
let decrypted = protocol.decrypt_key(&encrypted, &device_b_privkey)?;

Cross-Platform Compatibility

// Example: Interoperating with other X25519 implementations
let protocol = X25519Protocol::new();

// Generate keys compatible with other libraries
let (private_key, public_key) = protocol.generate_keypair()?;

// Export in standard format
let private_key_hex = hex::encode(&private_key);
let public_key_hex = hex::encode(&public_key);

// Can be imported by other X25519 implementations

Limitations

No Signature Support

X25519 protocol does not support signatures:

• Key Exchange Only: Designed for key agreement, not signing

• Use Ed25519: For signatures, use Ed25519 (same curve, different algorithm)

• Hybrid Approach: Combine X25519 for key exchange with Ed25519 for signatures

Key Size Limitations

• Fixed Key Size: All keys are exactly 32 bytes

• No Variable Length: Cannot use different key sizes

• Standard Compliance: Follows RFC 7748 specifications

Protocol Isolation

• No Cross-Protocol: Cannot mix with other protocols in single operation

• Separate Instances: Each protocol requires separate implementation

• Unified Interface: Use Privacy Engine for multi-protocol support