Advanced Cryptography

Post-quantum cryptography, homomorphic encryption, zero-knowledge proofs, and advanced protocols.

Overview

Advanced cryptography addresses emerging security challenges.

Post-Quantum Cryptography

Zero-Knowledge Proofs

# Simple ZKP concept
class ZeroKnowledgeProof:
    def __init__(self, secret):
        self.secret = secret
    
    def commit(self):
        # Generate random commitment
        self.r = random.randint(0, P-1)
        commitment = pow(G, self.r, P)
        return commitment
    
    def prove(self, challenge):
        # Generate response
        response = (self.r + challenge * self.secret) % Q
        return response
    
    def verify(self, commitment, challenge, response):
        # Verify proof
        left = pow(G, response, P)
        right = (commitment * pow(Y, challenge, P)) % P
        return left == right

Homomorphic Encryption

# Conceptual HE operations
class HomomorphicEncryption:
    def encrypt(self, plaintext):
        # Encrypt data
        return encrypted_data
    
    def add(self, encrypted_a, encrypted_b):
        # Perform addition on encrypted data
        return encrypted_result
    
    def multiply(self, encrypted_a, scalar):
        # Perform multiplication on encrypted data
        return encrypted_result
    
    def decrypt(self, encrypted_result):
        # Decrypt result
        return plaintext

Advanced Protocols

Quantum Key Distribution

BB84 Protocol:
1. Alice sends polarized photons
2. Bob measures with random basis
3. They compare bases publicly
4. Keep matching results as key
5. Detect eavesdropping

Practice

Implement a simple zero-knowledge proof system.