quantum_enhanced_lwe.py

import numpy as np

class QuantumEnhancedLWE:
    def __init__(self, n=256, q=4093, sigma=1.0):
        """
        Initialize the Quantum Enhanced LWE system with specified parameters.
        :param n: Dimension of the lattice (default: 256)
        :param q: Modulus for the lattice (default: 4093)
        :param sigma: Standard deviation for error sampling (default: 1.0)
        """
        self.n = n
        self.q = q
        self.sigma = sigma

    def gen_keypair(self):
        """
        Generate a public and private key pair for encryption and decryption.
        :return: Tuple containing the public key and private key.
        """
        s = self.sample_uniform(self.n)
        e = self.sample_error(self.n)
        a = self.sample_uniform(self.n)
        b = (np.dot(a, s) + e) % self.q
        return (a, b), s

    def encrypt(self, pk, m):
        """
        Encrypt a message using the public key.
        :param pk: Public key
        :param m: Message to encrypt (0 or 1)
        :return: Ciphertext as a tuple of (a, c)
        """
        s, quantum_key = pk
        a = self.sample_uniform(self.n)
        e = self.sample_error(1)[0]
        b = (np.dot(a, s) + e) % self.q
        c = (b + m * (self.q // 4)) % self.q
        return a, c

    def decrypt(self, sk, ct):
        """
        Decrypt a ciphertext using the private key.
        :param sk: Private key
        :param ct: Ciphertext to decrypt
        :return: Decrypted message (0 or 1)
        """
        a, c = ct
        s = sk
        b = (np.dot(a, s)) % self.q
        m = (c - b) % self.q
        return 0 if m < self.q // 2 else 1

    def sample_uniform(self, size):
        """
        Sample a uniform random vector of given size.
        :param size: Size of the vector
        :return: Uniform random vector
        """
        return np.random.randint(0, self.q, size)

    def sample_error(self, size):
        """
        Sample an error vector from a Gaussian distribution.
        :param size: Size of the vector
        :return: Error vector
        """
        return np.random.normal(0, self.sigma, size).astype(int)

    def quantum_enhanced_encrypt(self, pk, m):
        """
        Encrypt a message using quantum-enhanced techniques.
        :param pk: Public key
        :param m: Message to encrypt (0 or 1)
        :return: Ciphertext as a tuple of (a, c)
        """
        # Initialize quantum state
        q_state = self.quantum_circuit.initialize_state()
        # Evolve state
        evolved_state = self.quantum_circuit.evolve_state(q_state, 1e-9)
        # Use evolved state amplitude as additional noise
        quantum_noise = np.abs(evolved_state[0])
        
        # Standard LWE encryption with quantum noise
        s, quantum_key = pk
        a = self.sample_uniform(self.n)
        e = self.sample_error(1)[0]
        e = (e + int(quantum_noise * self.q)) % self.q
        b = (np.dot(a, s) + e) % self.q
        c = (b + m * (self.q // 4)) % self.q
        return a, c

    def calculate_entangled_pairs(self):
        """
        Calculate the number of entangled pairs and their combinations.
        """
        return self.n * (self.n - 1) // 2

    def evaluate_evolutionary_potential(self, x, y):
        """
        Evaluate the evolutionary potential of a pair.
        :param x: First element of the pair
        :param y: Second element of the pair
        :return: Probability of successful evolution
        """
        return np.random.rand()  # Placeholder for actual probability calculation