Cryptography and Privacy Engineering: From Zero-Knowledge to Post-Quantum Security

┌─────────────────────────────────────────────────────────────┐
│                Modern Cryptographic Threats                │
├─────────────────────────────────────────────────────────────┤
│ Classical Attacks       │ → Brute force, cryptanalysis     │
│                        │   Side-channel attacks           │
│                        │   Implementation vulnerabilities │
├─────────────────────────────────────────────────────────────┤
│ Quantum Attacks        │ → Shor's algorithm (RSA/ECC)     │
│                        │   Grover's algorithm (AES)       │
│                        │   Quantum cryptanalysis          │
├─────────────────────────────────────────────────────────────┤
│ Privacy Attacks        │ → Linkability analysis           │
│                        │   Inference attacks              │
│                        │   De-anonymization techniques    │
├─────────────────────────────────────────────────────────────┤
│ AI-Enhanced Attacks    │ → ML-based cryptanalysis         │
│                        │   Automated vulnerability discovery│
│                        │   Adversarial AI techniques      │
└─────────────────────────────────────────────────────────────┘

#!/usr/bin/env python3
"""
Zero-Knowledge Proof Implementation Framework
Advanced ZKP systems for privacy-preserving applications
"""

import hashlib
import random
import json
from typing import Tuple, List, Dict, Any
from dataclasses import dataclass
from abc import ABC, abstractmethod

@dataclass
class ZKProof:
    """Zero-knowledge proof structure"""
    commitment: bytes
    challenge: bytes
    response: bytes
    public_parameters: Dict[str, Any]
    
class ZKProofSystem(ABC):
    """Abstract base class for ZK proof systems"""
    
    @abstractmethod
    def setup(self, security_parameter: int) -> Dict[str, Any]:
        """Generate public parameters"""
        pass
    
    @abstractmethod
    def prove(self, statement: Any, witness: Any, public_params: Dict[str, Any]) -> ZKProof:
        """Generate zero-knowledge proof"""
        pass
    
    @abstractmethod
    def verify(self, statement: Any, proof: ZKProof) -> bool:
        """Verify zero-knowledge proof"""
        pass

class SchnorrZKP(ZKProofSystem):
    """Schnorr Zero-Knowledge Proof implementation"""
    
    def __init__(self):
        # Use safe prime for demonstration (in practice, use standardized groups)
        self.p = 0x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
        self.g = 2
        self.q = (self.p - 1) // 2  # Order of subgroup
    
    def setup(self, security_parameter: int = 256) -> Dict[str, Any]:
        """Setup Schnorr proof system parameters"""
        return {
            "p": self.p,
            "g": self.g,
            "q": self.q,
            "security_parameter": security_parameter
        }
    
    def prove(self, statement: int, witness: int, public_params: Dict[str, Any]) -> ZKProof:
        """
        Generate Schnorr proof for discrete logarithm knowledge
        Statement: y = g^x mod p
        Witness: x (secret exponent)
        """
        p, g, q = public_params["p"], public_params["g"], public_params["q"]
        
        # Commitment phase: choose random r, compute A = g^r mod p
        r = random.randint(1, q - 1)
        commitment = pow(g, r, p)
        
        # Challenge phase: compute challenge as hash of public info
        challenge_input = f"{statement}_{commitment}_{g}_{p}".encode()
        challenge = int(hashlib.sha256(challenge_input).hexdigest(), 16) % q
        
        # Response phase: compute s = r + c*x mod q
        response = (r + challenge * witness) % q
        
        return ZKProof(
            commitment=commitment.to_bytes((p.bit_length() + 7) // 8, 'big'),
            challenge=challenge.to_bytes(32, 'big'),
            response=response.to_bytes((q.bit_length() + 7) // 8, 'big'),
            public_parameters=public_params
        )
    
    def verify(self, statement: int, proof: ZKProof) -> bool:
        """Verify Schnorr proof"""
        try:
            p = proof.public_parameters["p"]
            g = proof.public_parameters["g"]
            q = proof.public_parameters["q"]
            
            # Extract proof components
            commitment = int.from_bytes(proof.commitment, 'big')
            challenge = int.from_bytes(proof.challenge, 'big')
            response = int.from_bytes(proof.response, 'big')
            
            # Verify challenge is correctly computed
            challenge_input = f"{statement}_{commitment}_{g}_{p}".encode()
            expected_challenge = int(hashlib.sha256(challenge_input).hexdigest(), 16) % q
            
            if challenge != expected_challenge:
                return False
            
            # Verify proof equation: g^s = A * y^c mod p
            left_side = pow(g, response, p)
            right_side = (commitment * pow(statement, challenge, p)) % p
            
            return left_side == right_side
            
        except Exception as e:
            print(f"Verification error: {e}")
            return False

class BulletproofRangeProof:
    """Bulletproof range proof implementation (simplified)"""
    
    def __init__(self, bit_length: int = 64):
        self.bit_length = bit_length
        self.setup_parameters()
    
    def setup_parameters(self):
        """Setup Bulletproof parameters"""
        # Simplified elliptic curve parameters (use proper curve in production)
        self.p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F
        self.n = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141
        
        # Generator points (simplified - use proper curve points)
        self.G = (0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798,
                  0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8)
        self.H = (0xC6047F9441ED7D6D3045406E95C07CD85C778E4B8CEF3CA7ABAC09B95C709EE5,
                  0x1AE168FEA63DC339A3C58419466CEAEEF7F632653266D0E1236431A950CFE52A)
    
    def prove_range(self, value: int, randomness: int) -> Dict[str, Any]:
        """
        Generate range proof for value in [0, 2^bit_length)
        Returns simplified proof structure
        """
        if value < 0 or value >= 2**self.bit_length:
            raise ValueError(f"Value must be in range [0, {2**self.bit_length})")
        
        # Convert value to binary representation
        binary_repr = [(value >> i) & 1 for i in range(self.bit_length)]
        
        # Generate commitments for each bit
        bit_commitments = []
        bit_randomness = []
        
        for bit in binary_repr:
            r = random.randint(1, self.n - 1)
            bit_randomness.append(r)
            
            # Simplified commitment: C = bit * G + r * H (using scalar representation)
            commitment = (bit * self.G[0] + r * self.H[0]) % self.p
            bit_commitments.append(commitment)
        
        # Generate proof of bit validity (simplified)
        bit_proofs = []
        for i, (bit, r) in enumerate(zip(binary_repr, bit_randomness)):
            # Prove bit is 0 or 1 using Schnorr-like proof
            schnorr_zkp = SchnorrZKP()
            params = schnorr_zkp.setup()
            
            # Simplified bit proof
            bit_proof = {
                "commitment": bit_commitments[i],
                "is_valid_bit": True,  # Simplified - real implementation would have ZKP
                "randomness_commitment": r
            }
            bit_proofs.append(bit_proof)
        
        return {
            "type": "bulletproof_range",
            "bit_length": self.bit_length,
            "value_commitment": sum(bit_commitments) % self.p,
            "bit_commitments": bit_commitments,
            "bit_proofs": bit_proofs,
            "aggregated_proof": self.aggregate_bit_proofs(bit_proofs)
        }
    
    def verify_range_proof(self, proof: Dict[str, Any], public_commitment: int) -> bool:
        """Verify range proof"""
        try:
            # Verify bit commitments sum to public commitment
            computed_commitment = sum(proof["bit_commitments"]) % self.p
            
            if computed_commitment != public_commitment:
                return False
            
            # Verify each bit proof (simplified)
            for bit_proof in proof["bit_proofs"]:
                if not bit_proof["is_valid_bit"]:
                    return False
            
            # Verify aggregated proof
            return self.verify_aggregated_proof(proof["aggregated_proof"])
            
        except Exception as e:
            print(f"Range proof verification error: {e}")
            return False
    
    def aggregate_bit_proofs(self, bit_proofs: List[Dict[str, Any]]) -> Dict[str, Any]:
        """Aggregate individual bit proofs (simplified)"""
        return {
            "aggregated": True,
            "proof_size_reduction": len(bit_proofs) * 0.7,  # Simplified metric
            "verification_time": len(bit_proofs) * 0.1  # Simplified metric
        }
    
    def verify_aggregated_proof(self, aggregated_proof: Dict[str, Any]) -> bool:
        """Verify aggregated proof (simplified)"""
        return aggregated_proof.get("aggregated", False)

class ZKSNARKSystem:
    """zk-SNARK implementation framework (simplified)"""
    
    def __init__(self):
        self.setup_done = False
        self.proving_key = None
        self.verification_key = None
    
    def trusted_setup(self, circuit_description: Dict[str, Any]) -> Tuple[Dict, Dict]:
        """
        Perform trusted setup for zk-SNARK
        WARNING: This is a simplified version - real implementation requires
        secure multiparty computation for setup
        """
        # Generate random toxic waste (should be deleted after setup)
        tau = random.randint(1, 2**256)
        alpha = random.randint(1, 2**256)
        beta = random.randint(1, 2**256)
        gamma = random.randint(1, 2**256)
        
        # Setup parameters based on circuit
        circuit_size = circuit_description.get("num_constraints", 100)
        
        # Proving key (simplified structure)
        proving_key = {
            "alpha": alpha,
            "beta": beta,
            "circuit_size": circuit_size,
            "constraint_system": circuit_description,
            "toxic_waste_used": True  # In real implementation, this would be deleted
        }
        
        # Verification key (public)
        verification_key = {
            "gamma": gamma,
            "circuit_hash": hashlib.sha256(str(circuit_description).encode()).hexdigest(),
            "public_inputs_count": circuit_description.get("public_inputs", 0)
        }
        
        self.proving_key = proving_key
        self.verification_key = verification_key
        self.setup_done = True
        
        return proving_key, verification_key
    
    def generate_proof(self, public_inputs: List[int], private_witness: List[int]) -> Dict[str, Any]:
        """Generate zk-SNARK proof"""
        if not self.setup_done:
            raise RuntimeError("Trusted setup must be performed first")
        
        # Simulate constraint satisfaction
        if not self.check_constraint_satisfaction(public_inputs, private_witness):
            raise ValueError("Constraint system not satisfied")
        
        # Generate proof components (simplified)
        proof = {
            "A": self.compute_proof_element_A(private_witness),
            "B": self.compute_proof_element_B(private_witness),
            "C": self.compute_proof_element_C(private_witness),
            "public_inputs": public_inputs,
            "proof_size": 3 * 32,  # Simplified: 3 group elements of 32 bytes each
            "generation_time": len(private_witness) * 0.01  # Simplified timing
        }
        
        return proof
    
    def verify_proof(self, proof: Dict[str, Any]) -> bool:
        """Verify zk-SNARK proof"""
        if not self.setup_done:
            return False
        
        try:
            # Verify proof equation (simplified)
            # Real implementation would use elliptic curve pairing
            A = proof["A"]
            B = proof["B"] 
            C = proof["C"]
            
            # Simplified verification equation
            verification_result = (A * B) % (2**256) == C % (2**256)
            
            return verification_result
            
        except Exception as e:
            print(f"SNARK verification error: {e}")
            return False
    
    def check_constraint_satisfaction(self, public_inputs: List[int], private_witness: List[int]) -> bool:
        """Check if inputs satisfy circuit constraints (simplified)"""
        # Simplified constraint checking
        if len(public_inputs) + len(private_witness) < self.proving_key["circuit_size"]:
            return False
        
        # Example constraint: sum of inputs equals first public input
        total_sum = sum(public_inputs[1:]) + sum(private_witness)
        return total_sum == public_inputs[0]
    
    def compute_proof_element_A(self, witness: List[int]) -> int:
        """Compute proof element A (simplified)"""
        return sum(w * (i + 1) for i, w in enumerate(witness)) % (2**256)
    
    def compute_proof_element_B(self, witness: List[int]) -> int:
        """Compute proof element B (simplified)"""
        return sum(w * w for w in witness) % (2**256)
    
    def compute_proof_element_C(self, witness: List[int]) -> int:
        """Compute proof element C (simplified)"""
        A = self.compute_proof_element_A(witness)
        B = self.compute_proof_element_B(witness)
        return (A * B) % (2**256)

def demonstrate_zkp_applications():
    """Demonstrate practical ZKP applications"""
    
    applications = {
        "private_voting": {
            "description": "Anonymous voting with verifiable tallies",
            "zkp_type": "Range proofs + NIZKs",
            "privacy_guarantee": "Vote secrecy",
            "verifiability": "Public tally verification"
        },
        
        "credential_verification": {
            "description": "Prove credential validity without revealing credential",
            "zkp_type": "zk-SNARKs",
            "privacy_guarantee": "Credential privacy",
            "use_cases": ["Age verification", "Qualification proof", "Access control"]
        },
        
        "financial_privacy": {
            "description": "Private transactions with public auditability",
            "zkp_type": "Bulletproofs + zk-STARKs",
            "privacy_guarantee": "Transaction amount privacy",
            "compliance": "Regulatory reporting without data exposure"
        },
        
        "supply_chain_verification": {
            "description": "Prove supply chain compliance without revealing trade secrets",
            "zkp_type": "Merkle tree proofs + NIZKs",
            "privacy_guarantee": "Process confidentiality",
            "verification": "Compliance without data sharing"
        },
        
        "identity_systems": {
            "description": "Self-sovereign identity with selective disclosure",
            "zkp_type": "CL signatures + zk-SNARKs",
            "privacy_guarantee": "Attribute privacy",
            "features": ["Selective disclosure", "Unlinkable presentations", "Revocation"]
        }
    }
    
    return applications

#!/usr/bin/env python3
"""
Homomorphic Encryption Implementation Framework
Privacy-preserving computation on encrypted data
"""

import random
import math
from typing import List, Tuple, Union
from dataclasses import dataclass

@dataclass
class HECiphertext:
    """Homomorphic encryption ciphertext"""
    data: Union[int, List[int]]
    noise_level: float
    scheme: str
    
@dataclass
class HEPublicKey:
    """Homomorphic encryption public key"""
    n: int  # Modulus
    g: int  # Generator (for some schemes)
    scheme: str

@dataclass
class HEPrivateKey:
    """Homomorphic encryption private key"""
    lambda_val: int
    mu: int
    scheme: str

class PaillierHE:
    """Paillier homomorphic encryption (additively homomorphic)"""
    
    def __init__(self, key_size: int = 2048):
        self.key_size = key_size
        self.public_key = None
        self.private_key = None
    
    def generate_keypair(self) -> Tuple[HEPublicKey, HEPrivateKey]:
        """Generate Paillier key pair"""
        # Generate two large primes
        p = self._generate_prime(self.key_size // 2)
        q = self._generate_prime(self.key_size // 2)
        
        n = p * q
        lambda_val = self._lcm(p - 1, q - 1)
        
        # Choose generator g
        g = n + 1  # Common choice for efficiency
        
        # Compute mu = (L(g^lambda mod n^2))^(-1) mod n
        # where L(x) = (x - 1) / n
        g_lambda = pow(g, lambda_val, n * n)
        l_result = (g_lambda - 1) // n
        mu = self._mod_inverse(l_result, n)
        
        public_key = HEPublicKey(n=n, g=g, scheme="paillier")
        private_key = HEPrivateKey(lambda_val=lambda_val, mu=mu, scheme="paillier")
        
        self.public_key = public_key
        self.private_key = private_key
        
        return public_key, private_key
    
    def encrypt(self, plaintext: int, public_key: HEPublicKey = None) -> HECiphertext:
        """Encrypt plaintext using Paillier encryption"""
        if public_key is None:
            public_key = self.public_key
        
        if public_key is None:
            raise ValueError("Public key not provided")
        
        n = public_key.n
        g = public_key.g
        
        # Choose random r coprime to n
        r = self._random_coprime(n)
        
        # Compute ciphertext: c = g^m * r^n mod n^2
        ciphertext = (pow(g, plaintext, n * n) * pow(r, n, n * n)) % (n * n)
        
        return HECiphertext(
            data=ciphertext,
            noise_level=0.0,  # Paillier is exact
            scheme="paillier"
        )
    
    def decrypt(self, ciphertext: HECiphertext, private_key: HEPrivateKey = None) -> int:
        """Decrypt Paillier ciphertext"""
        if private_key is None:
            private_key = self.private_key
        
        if private_key is None:
            raise ValueError("Private key not provided")
        
        n = self.public_key.n
        lambda_val = private_key.lambda_val
        mu = private_key.mu
        
        # Compute c^lambda mod n^2
        c_lambda = pow(ciphertext.data, lambda_val, n * n)
        
        # Apply L function: L(x) = (x - 1) / n
        l_result = (c_lambda - 1) // n
        
        # Compute plaintext: m = L(c^lambda mod n^2) * mu mod n
        plaintext = (l_result * mu) % n
        
        return plaintext
    
    def add_encrypted(self, ct1: HECiphertext, ct2: HECiphertext) -> HECiphertext:
        """Homomorphic addition of encrypted values"""
        if ct1.scheme != "paillier" or ct2.scheme != "paillier":
            raise ValueError("Ciphertexts must be Paillier encrypted")
        
        n = self.public_key.n
        
        # Homomorphic addition: E(m1) * E(m2) mod n^2 = E(m1 + m2)
        result_data = (ct1.data * ct2.data) % (n * n)
        
        return HECiphertext(
            data=result_data,
            noise_level=max(ct1.noise_level, ct2.noise_level),
            scheme="paillier"
        )
    
    def multiply_by_constant(self, ciphertext: HECiphertext, constant: int) -> HECiphertext:
        """Homomorphic multiplication by plaintext constant"""
        n = self.public_key.n
        
        # E(m)^k mod n^2 = E(k * m)
        result_data = pow(ciphertext.data, constant, n * n)
        
        return HECiphertext(
            data=result_data,
            noise_level=ciphertext.noise_level,
            scheme="paillier"
        )
    
    def _generate_prime(self, bits: int) -> int:
        """Generate random prime of specified bit length (simplified)"""
        while True:
            candidate = random.getrandbits(bits)
            candidate |= (1 << bits - 1) | 1  # Ensure it's odd and has correct bit length
            if self._is_prime(candidate):
                return candidate
    
    def _is_prime(self, n: int, k: int = 10) -> bool:
        """Miller-Rabin primality test"""
        if n < 2:
            return False
        if n == 2 or n == 3:
            return True
        if n % 2 == 0:
            return False
        
        # Write n-1 as d * 2^r
        r = 0
        d = n - 1
        while d % 2 == 0:
            r += 1
            d //= 2
        
        # Perform k rounds of testing
        for _ in range(k):
            a = random.randrange(2, n - 1)
            x = pow(a, d, n)
            
            if x == 1 or x == n - 1:
                continue
            
            for _ in range(r - 1):
                x = pow(x, 2, n)
                if x == n - 1:
                    break
            else:
                return False
        
        return True
    
    def _lcm(self, a: int, b: int) -> int:
        """Compute least common multiple"""
        return abs(a * b) // math.gcd(a, b)
    
    def _mod_inverse(self, a: int, m: int) -> int:
        """Compute modular inverse using extended Euclidean algorithm"""
        if math.gcd(a, m) != 1:
            raise ValueError("Modular inverse does not exist")
        
        def extended_gcd(a, b):
            if a == 0:
                return b, 0, 1
            gcd, x1, y1 = extended_gcd(b % a, a)
            x = y1 - (b // a) * x1
            y = x1
            return gcd, x, y
        
        _, x, _ = extended_gcd(a % m, m)
        return x % m
    
    def _random_coprime(self, n: int) -> int:
        """Generate random number coprime to n"""
        while True:
            r = random.randrange(1, n)
            if math.gcd(r, n) == 1:
                return r

class CKKSHE:
    """CKKS homomorphic encryption (approximate, supports floating point)"""
    
    def __init__(self, polynomial_degree: int = 8192, coefficient_modulus_bits: int = 438):
        self.polynomial_degree = polynomial_degree
        self.coefficient_modulus_bits = coefficient_modulus_bits
        self.scaling_factor = 2**40  # For precision control
        self.setup_parameters()
    
    def setup_parameters(self):
        """Setup CKKS parameters (simplified)"""
        # In real implementation, would use Number Theoretic Transform (NTT) friendly primes
        self.modulus = 2**self.coefficient_modulus_bits - 1
        self.primitive_root = self._find_primitive_root(self.polynomial_degree)
        
    def generate_keypair(self) -> Tuple[dict, dict]:
        """Generate CKKS key pair (simplified)"""
        # Generate secret key as polynomial with small coefficients
        secret_key = [random.randint(-1, 1) for _ in range(self.polynomial_degree)]
        
        # Generate public key (a, b) where b = a*s + e
        a = [random.randint(0, self.modulus - 1) for _ in range(self.polynomial_degree)]
        error = [random.gauss(0, 3.2) for _ in range(self.polynomial_degree)]  # Gaussian error
        
        b = [(a[i] * secret_key[i] + int(error[i])) % self.modulus 
             for i in range(self.polynomial_degree)]
        
        public_key = {"a": a, "b": b}
        private_key = {"s": secret_key}
        
        return public_key, private_key
    
    def encode(self, values: List[float]) -> List[int]:
        """Encode floating point values into polynomial coefficients"""
        if len(values) > self.polynomial_degree // 2:
            raise ValueError("Too many values to encode")
        
        # Pad with zeros if necessary
        while len(values) < self.polynomial_degree // 2:
            values.append(0.0)
        
        # Scale and round to integers
        scaled_values = [int(v * self.scaling_factor) for v in values]
        
        # Embed into polynomial using complex encoding (simplified)
        polynomial = scaled_values + [0] * (self.polynomial_degree - len(scaled_values))
        
        return polynomial
    
    def decode(self, polynomial: List[int]) -> List[float]:
        """Decode polynomial coefficients back to floating point values"""
        # Extract the first half (real parts in simplified encoding)
        scaled_values = polynomial[:self.polynomial_degree // 2]
        
        # Unscale to floating point
        values = [v / self.scaling_factor for v in scaled_values]
        
        return values
    
    def encrypt(self, plaintext_poly: List[int], public_key: dict) -> dict:
        """Encrypt polynomial using CKKS (simplified)"""
        a, b = public_key["a"], public_key["b"]
        
        # Generate random polynomial u with small coefficients
        u = [random.randint(-1, 1) for _ in range(self.polynomial_degree)]
        
        # Generate error polynomials
        e0 = [random.gauss(0, 3.2) for _ in range(self.polynomial_degree)]
        e1 = [random.gauss(0, 3.2) for _ in range(self.polynomial_degree)]
        
        # Compute ciphertext (c0, c1)
        c0 = [(b[i] * u[i] + int(e0[i]) + plaintext_poly[i]) % self.modulus 
              for i in range(self.polynomial_degree)]
        c1 = [(a[i] * u[i] + int(e1[i])) % self.modulus 
              for i in range(self.polynomial_degree)]
        
        return {
            "c0": c0,
            "c1": c1,
            "noise_budget": self.coefficient_modulus_bits - 20  # Simplified noise tracking
        }
    
    def decrypt(self, ciphertext: dict, private_key: dict) -> List[int]:
        """Decrypt CKKS ciphertext (simplified)"""
        c0, c1 = ciphertext["c0"], ciphertext["c1"]
        s = private_key["s"]
        
        # Compute c0 + c1 * s
        decrypted = [(c0[i] + c1[i] * s[i]) % self.modulus 
                    for i in range(self.polynomial_degree)]
        
        return decrypted
    
    def add_encrypted(self, ct1: dict, ct2: dict) -> dict:
        """Homomorphic addition of CKKS ciphertexts"""
        c0_result = [(ct1["c0"][i] + ct2["c0"][i]) % self.modulus 
                     for i in range(self.polynomial_degree)]
        c1_result = [(ct1["c1"][i] + ct2["c1"][i]) % self.modulus 
                     for i in range(self.polynomial_degree)]
        
        return {
            "c0": c0_result,
            "c1": c1_result,
            "noise_budget": min(ct1["noise_budget"], ct2["noise_budget"]) - 1
        }
    
    def multiply_encrypted(self, ct1: dict, ct2: dict) -> dict:
        """Homomorphic multiplication of CKKS ciphertexts (simplified)"""
        # Real implementation requires relinearization
        # This is a simplified version
        
        c0_result = [(ct1["c0"][i] * ct2["c0"][i]) % self.modulus 
                     for i in range(self.polynomial_degree)]
        c1_result = [(ct1["c1"][i] * ct2["c1"][i]) % self.modulus 
                     for i in range(self.polynomial_degree)]
        
        return {
            "c0": c0_result,
            "c1": c1_result,
            "noise_budget": min(ct1["noise_budget"], ct2["noise_budget"]) - 5  # Noise grows faster
        }
    
    def _find_primitive_root(self, n: int) -> int:
        """Find primitive nth root of unity (simplified)"""
        # In real implementation, would use NTT-friendly parameters
        return 3  # Simplified placeholder

def demonstrate_privacy_preserving_ml():
    """Demonstrate privacy-preserving machine learning using HE"""
    
    # Initialize CKKS for floating point computation
    ckks = CKKSHE()
    public_key, private_key = ckks.generate_keypair()
    
    # Example: Private neural network inference
    def private_neural_network_inference():
        # Input data (encrypted)
        input_data = [1.5, 2.3, -0.8, 1.2]
        encoded_input = ckks.encode(input_data)
        encrypted_input = ckks.encrypt(encoded_input, public_key)
        
        # Model weights (can be public or encrypted)
        weights = [0.5, -0.3, 0.8, 0.2]
        encoded_weights = ckks.encode(weights)
        encrypted_weights = ckks.encrypt(encoded_weights, public_key)
        
        # Homomorphic computation: dot product
        encrypted_result = ckks.multiply_encrypted(encrypted_input, encrypted_weights)
        
        # Decrypt result
        decrypted_poly = ckks.decrypt(encrypted_result, private_key)
        result = ckks.decode(decrypted_poly)
        
        return {
            "input_privacy": "Preserved",
            "computation": "Homomorphic",
            "result": result[0],  # First element of result
            "noise_level": encrypted_result["noise_budget"]
        }
    
    # Example: Private statistical analysis
    def private_statistics():
        # Dataset (encrypted)
        dataset = [10.5, 20.3, 15.8, 25.2, 18.7]
        encoded_data = ckks.encode(dataset)
        encrypted_data = ckks.encrypt(encoded_data, public_key)
        
        # Compute encrypted sum (simplified)
        encrypted_sum = encrypted_data
        for _ in range(len(dataset) - 1):
            encrypted_sum = ckks.add_encrypted(encrypted_sum, encrypted_data)
        
        # Decrypt sum
        decrypted_sum_poly = ckks.decrypt(encrypted_sum, private_key)
        sum_result = ckks.decode(decrypted_sum_poly)
        
        return {
            "operation": "Sum computation on encrypted data",
            "privacy_guarantee": "Individual values never revealed",
            "result": sum_result[0] / len(dataset),  # Average
            "data_size": len(dataset)
        }
    
    return {
        "neural_network": private_neural_network_inference(),
        "statistics": private_statistics(),
        "capabilities": [
            "Private model inference",
            "Encrypted statistical analysis", 
            "Secure multi-party computation",
            "Privacy-preserving analytics"
        ]
    }

#!/usr/bin/env python3
"""
Post-Quantum Cryptography Implementation Framework
Quantum-resistant cryptographic algorithms
"""

import hashlib
import random
import numpy as np
from typing import Tuple, List, Dict, Any
from dataclasses import dataclass

@dataclass
class LatticeKey:
    """Lattice-based cryptographic key"""
    matrix: np.ndarray
    error_distribution: str
    security_parameter: int

@dataclass
class PostQuantumSignature:
    """Post-quantum digital signature"""
    signature: bytes
    algorithm: str
    security_level: int

class NTRU:
    """NTRU lattice-based encryption (simplified implementation)"""
    
    def __init__(self, n: int = 509, p: int = 3, q: int = 2048):
        """
        Initialize NTRU parameters
        n: polynomial degree
        p, q: moduli (p < q, gcd(p,q) = 1)
        """
        self.n = n
        self.p = p
        self.q = q
        self.public_key = None
        self.private_key = None
    
    def generate_keypair(self) -> Tuple[Dict[str, Any], Dict[str, Any]]:
        """Generate NTRU key pair"""
        # Generate private key polynomials f and g
        f = self._generate_small_polynomial()
        g = self._generate_small_polynomial()
        
        # Ensure f is invertible modulo p and q
        while not self._is_invertible(f, self.p) or not self._is_invertible(f, self.q):
            f = self._generate_small_polynomial()
        
        # Compute f^(-1) mod p and f^(-1) mod q
        f_inv_p = self._polynomial_inverse(f, self.p)
        f_inv_q = self._polynomial_inverse(f, self.q)
        
        # Compute public key h = g * f^(-1) mod q
        h = self._polynomial_multiply(g, f_inv_q, self.q)
        
        public_key = {
            "h": h,
            "n": self.n,
            "p": self.p,
            "q": self.q
        }
        
        private_key = {
            "f": f,
            "f_inv_p": f_inv_p,
            "g": g
        }
        
        self.public_key = public_key
        self.private_key = private_key
        
        return public_key, private_key
    
    def encrypt(self, message: List[int], public_key: Dict[str, Any] = None) -> List[int]:
        """Encrypt message using NTRU"""
        if public_key is None:
            public_key = self.public_key
        
        h = public_key["h"]
        
        # Generate random polynomial r
        r = self._generate_small_polynomial()
        
        # Compute ciphertext e = r * h + m mod q
        rh = self._polynomial_multiply(r, h, self.q)
        ciphertext = [(rh[i] + message[i]) % self.q for i in range(self.n)]
        
        return ciphertext
    
    def decrypt(self, ciphertext: List[int], private_key: Dict[str, Any] = None) -> List[int]:
        """Decrypt NTRU ciphertext"""
        if private_key is None:
            private_key = self.private_key
        
        f = private_key["f"]
        f_inv_p = private_key["f_inv_p"]
        
        # Compute a = f * e mod q
        a = self._polynomial_multiply(f, ciphertext, self.q)
        
        # Reduce a modulo p
        a_mod_p = [a[i] % self.p for i in range(self.n)]
        
        # Compute message m = a * f^(-1) mod p
        message = self._polynomial_multiply(a_mod_p, f_inv_p, self.p)
        
        return message
    
    def _generate_small_polynomial(self) -> List[int]:
        """Generate polynomial with small coefficients"""
        # Generate polynomial with coefficients in {-1, 0, 1}
        return [random.choice([-1, 0, 1]) for _ in range(self.n)]
    
    def _polynomial_multiply(self, a: List[int], b: List[int], modulus: int) -> List[int]:
        """Multiply polynomials in ring Z[x]/(x^n - 1, modulus)"""
        result = [0] * self.n
        
        for i in range(self.n):
            for j in range(self.n):
                # Convolution with wraparound (x^n = 1)
                k = (i + j) % self.n
                result[k] = (result[k] + a[i] * b[j]) % modulus
        
        return result
    
    def _is_invertible(self, poly: List[int], modulus: int) -> bool:
        """Check if polynomial is invertible modulo given modulus (simplified)"""
        # Simplified check - in practice would use extended Euclidean algorithm
        return True  # Placeholder
    
    def _polynomial_inverse(self, poly: List[int], modulus: int) -> List[int]:
        """Compute polynomial inverse (simplified implementation)"""
        # Simplified inverse computation - real implementation uses extended Euclidean algorithm
        # This is a placeholder that returns a valid-looking polynomial
        return [(i + 1) % modulus for i in range(self.n)]

class DilithiumSignature:
    """Dilithium post-quantum signature scheme (simplified)"""
    
    def __init__(self, security_level: int = 3):
        """
        Initialize Dilithium parameters
        security_level: 1-5 (higher = more secure but slower)
        """
        self.security_level = security_level
        self.setup_parameters()
    
    def setup_parameters(self):
        """Setup Dilithium parameters based on security level"""
        if self.security_level == 3:
            self.n = 256
            self.q = 8380417
            self.d = 13
            self.tau = 49
            self.gamma1 = (1 << 19)
            self.gamma2 = (self.q - 1) // 32
            self.k = 6  # Number of rows in A
            self.l = 5  # Number of columns in A
        else:
            # Default parameters
            self.n = 256
            self.q = 8380417
            self.d = 13
            self.tau = 49
            self.gamma1 = (1 << 19)
            self.gamma2 = (self.q - 1) // 32
            self.k = 4
            self.l = 4
    
    def generate_keypair(self) -> Tuple[Dict[str, Any], Dict[str, Any]]:
        """Generate Dilithium key pair"""
        # Generate random seed
        seed = random.randbytes(32)
        
        # Generate matrix A from seed (would use SHAKE-128 in real implementation)
        A = self._generate_matrix_A(seed)
        
        # Generate secret vectors s1, s2
        s1 = self._generate_secret_vector(self.l)
        s2 = self._generate_secret_vector(self.k)
        
        # Compute t = A * s1 + s2
        t = self._matrix_vector_multiply(A, s1)
        t = self._vector_add(t, s2)
        
        # Public key
        public_key = {
            "A_seed": seed,
            "t": t,
            "security_level": self.security_level
        }
        
        # Private key
        private_key = {
            "s1": s1,
            "s2": s2,
            "t": t
        }
        
        return public_key, private_key
    
    def sign(self, message: bytes, private_key: Dict[str, Any]) -> PostQuantumSignature:
        """Generate Dilithium signature"""
        s1 = private_key["s1"]
        s2 = private_key["s2"]
        
        # Hash message (simplified)
        message_hash = hashlib.sha256(message).digest()
        
        # Generate random y
        y = self._generate_random_vector(self.l)
        
        # Compute w = A * y (need to reconstruct A from public key)
        # This is simplified - real implementation maintains A
        A = np.random.randint(0, self.q, size=(self.k, self.l))  # Placeholder
        w = self._matrix_vector_multiply(A, y)
        
        # Compute challenge c from message hash and w
        c = self._compute_challenge(message_hash, w)
        
        # Compute z = y + c * s1
        cs1 = self._scalar_vector_multiply(c, s1)
        z = self._vector_add(y, cs1)
        
        # Rejection sampling (simplified)
        if self._norm(z) > self.gamma1 - 1:
            # Restart with new y (simplified - just continue)
            pass
        
        # Compute hint h (simplified)
        h = self._compute_hint(s2, c, w)
        
        # Signature is (z, h, c)
        signature_data = {
            "z": z,
            "h": h,
            "c": c
        }
        
        # Serialize signature (simplified)
        signature_bytes = str(signature_data).encode()
        
        return PostQuantumSignature(
            signature=signature_bytes,
            algorithm="Dilithium",
            security_level=self.security_level
        )
    
    def verify(self, message: bytes, signature: PostQuantumSignature, public_key: Dict[str, Any]) -> bool:
        """Verify Dilithium signature"""
        try:
            # Deserialize signature (simplified)
            signature_data = eval(signature.signature.decode())
            z = signature_data["z"]
            h = signature_data["h"]
            c = signature_data["c"]
            
            # Reconstruct A from seed
            A = self._generate_matrix_A(public_key["A_seed"])
            t = public_key["t"]
            
            # Hash message
            message_hash = hashlib.sha256(message).digest()
            
            # Verify signature equation (simplified)
            # Real verification: Az - ct = w' and check h is correct
            Az = self._matrix_vector_multiply(A, z)
            ct = self._scalar_vector_multiply(c, t)
            w_prime = self._vector_subtract(Az, ct)
            
            # Verify challenge (simplified)
            expected_c = self._compute_challenge(message_hash, w_prime)
            
            return c == expected_c
            
        except Exception as e:
            print(f"Signature verification error: {e}")
            return False
    
    def _generate_matrix_A(self, seed: bytes) -> np.ndarray:
        """Generate matrix A from seed (simplified)"""
        # Real implementation would use SHAKE-128
        random.seed(int.from_bytes(seed[:4], 'big'))
        return np.random.randint(0, self.q, size=(self.k, self.l))
    
    def _generate_secret_vector(self, length: int) -> List[int]:
        """Generate secret vector with small coefficients"""
        return [random.randint(-self.tau, self.tau) for _ in range(length)]
    
    def _generate_random_vector(self, length: int) -> List[int]:
        """Generate random vector"""
        return [random.randint(0, self.gamma1 - 1) for _ in range(length)]
    
    def _matrix_vector_multiply(self, matrix: np.ndarray, vector: List[int]) -> List[int]:
        """Multiply matrix by vector modulo q"""
        result = matrix.dot(vector) % self.q
        return result.tolist()
    
    def _vector_add(self, a: List[int], b: List[int]) -> List[int]:
        """Add two vectors modulo q"""
        return [(a[i] + b[i]) % self.q for i in range(len(a))]
    
    def _vector_subtract(self, a: List[int], b: List[int]) -> List[int]:
        """Subtract two vectors modulo q"""
        return [(a[i] - b[i]) % self.q for i in range(len(a))]
    
    def _scalar_vector_multiply(self, scalar: int, vector: List[int]) -> List[int]:
        """Multiply vector by scalar modulo q"""
        return [(scalar * v) % self.q for v in vector]
    
    def _compute_challenge(self, message_hash: bytes, w: List[int]) -> int:
        """Compute challenge from hash and commitment (simplified)"""
        combined = message_hash + str(w).encode()
        return int.from_bytes(hashlib.sha256(combined).digest()[:4], 'big') % self.q
    
    def _compute_hint(self, s2: List[int], c: int, w: List[int]) -> List[int]:
        """Compute hint for signature (simplified)"""
        return [1 if random.random() < 0.1 else 0 for _ in range(len(w))]
    
    def _norm(self, vector: List[int]) -> int:
        """Compute infinity norm of vector"""
        return max(abs(v) for v in vector)

class SPHINCS:
    """SPHINCS+ hash-based signature scheme (simplified)"""
    
    def __init__(self, security_parameter: int = 128):
        self.security_parameter = security_parameter
        self.setup_parameters()
    
    def setup_parameters(self):
        """Setup SPHINCS+ parameters"""
        self.n = 32  # Hash output size (bytes)
        self.h = 64  # Height of hypertree
        self.d = 8   # Number of layers
        self.tree_height = self.h // self.d
        self.w = 16  # Winternitz parameter
    
    def generate_keypair(self) -> Tuple[Dict[str, Any], Dict[str, Any]]:
        """Generate SPHINCS+ key pair"""
        # Generate random seed
        seed = random.randbytes(self.n)
        
        # Generate secret key from seed
        sk_seed = hashlib.sha256(seed + b"SK").digest()
        sk_prf = hashlib.sha256(seed + b"PRF").digest()
        pub_seed = hashlib.sha256(seed + b"PUB").digest()
        
        # Compute public key root
        pk_root = self._compute_root(sk_seed, pub_seed)
        
        public_key = {
            "pk_root": pk_root,
            "pub_seed": pub_seed
        }
        
        private_key = {
            "sk_seed": sk_seed,
            "sk_prf": sk_prf,
            "pub_seed": pub_seed
        }
        
        return public_key, private_key
    
    def sign(self, message: bytes, private_key: Dict[str, Any]) -> PostQuantumSignature:
        """Generate SPHINCS+ signature"""
        sk_seed = private_key["sk_seed"]
        sk_prf = private_key["sk_prf"]
        pub_seed = private_key["pub_seed"]
        
        # Generate randomizer
        opt_rand = hashlib.sha256(sk_prf + message).digest()
        
        # Hash message with randomizer
        msg_hash = hashlib.sha256(opt_rand + message).digest()
        
        # Generate FORS signature
        fors_sig = self._fors_sign(msg_hash, sk_seed, pub_seed)
        
        # Generate hypertree signature
        ht_sig = self._ht_sign(fors_sig["pk"], sk_seed, pub_seed)
        
        # Combine signatures
        signature_data = {
            "randomizer": opt_rand,
            "fors_signature": fors_sig,
            "hypertree_signature": ht_sig
        }
        
        signature_bytes = json.dumps(signature_data, default=lambda x: x.hex() if isinstance(x, bytes) else x).encode()
        
        return PostQuantumSignature(
            signature=signature_bytes,
            algorithm="SPHINCS+",
            security_level=self.security_parameter
        )
    
    def verify(self, message: bytes, signature: PostQuantumSignature, public_key: Dict[str, Any]) -> bool:
        """Verify SPHINCS+ signature"""
        try:
            # Parse signature
            sig_data = json.loads(signature.signature.decode())
            
            # Recreate message hash
            opt_rand = bytes.fromhex(sig_data["randomizer"])
            msg_hash = hashlib.sha256(opt_rand + message).digest()
            
            # Verify FORS signature
            fors_pk = self._fors_verify(msg_hash, sig_data["fors_signature"], public_key["pub_seed"])
            
            # Verify hypertree signature
            verified_root = self._ht_verify(fors_pk, sig_data["hypertree_signature"], public_key["pub_seed"])
            
            # Check against public key
            return verified_root == public_key["pk_root"]
            
        except Exception as e:
            print(f"SPHINCS+ verification error: {e}")
            return False
    
    def _compute_root(self, sk_seed: bytes, pub_seed: bytes) -> bytes:
        """Compute root of hypertree (simplified)"""
        return hashlib.sha256(sk_seed + pub_seed + b"ROOT").digest()
    
    def _fors_sign(self, message: bytes, sk_seed: bytes, pub_seed: bytes) -> Dict[str, Any]:
        """Generate FORS signature (simplified)"""
        signature = []
        auth_paths = []
        
        # Generate FORS signature elements
        for i in range(self.w):
            sig_element = hashlib.sha256(sk_seed + message + i.to_bytes(4, 'big')).digest()
            signature.append(sig_element)
            
            # Generate authentication path (simplified)
            auth_path = [hashlib.sha256(sig_element + j.to_bytes(4, 'big')).digest() 
                        for j in range(self.tree_height)]
            auth_paths.append(auth_path)
        
        # Compute FORS public key
        fors_pk = hashlib.sha256(b"".join(signature)).digest()
        
        return {
            "signature": signature,
            "auth_paths": auth_paths,
            "pk": fors_pk
        }
    
    def _fors_verify(self, message: bytes, fors_sig: Dict[str, Any], pub_seed: bytes) -> bytes:
        """Verify FORS signature and return public key (simplified)"""
        return fors_sig["pk"]
    
    def _ht_sign(self, fors_pk: bytes, sk_seed: bytes, pub_seed: bytes) -> Dict[str, Any]:
        """Generate hypertree signature (simplified)"""
        return {
            "tree_signature": hashlib.sha256(fors_pk + sk_seed).digest(),
            "auth_path": [hashlib.sha256(fors_pk + i.to_bytes(4, 'big')).digest() 
                         for i in range(self.h)]
        }
    
    def _ht_verify(self, fors_pk: bytes, ht_sig: Dict[str, Any], pub_seed: bytes) -> bytes:
        """Verify hypertree signature (simplified)"""
        return hashlib.sha256(fors_pk + pub_seed + b"VERIFIED").digest()

def demonstrate_post_quantum_migration():
    """Demonstrate post-quantum cryptography migration strategies"""
    
    migration_strategies = {
        "hybrid_classical_pq": {
            "description": "Use both classical and post-quantum algorithms",
            "advantages": ["Backward compatibility", "Security against both threats"],
            "disadvantages": ["Increased overhead", "Complexity"],
            "use_cases": ["Transition period", "High-security applications"]
        },
        
        "crypto_agility": {
            "description": "Design systems to easily swap cryptographic algorithms",
            "principles": [
                "Algorithm abstraction layers",
                "Standardized interfaces",
                "Configuration-driven crypto selection",
                "Automated algorithm negotiation"
            ],
            "benefits": ["Future-proofing", "Quick response to threats"]
        },
        
        "pq_readiness_assessment": {
            "areas_to_evaluate": [
                "Current cryptographic inventory",
                "Performance impact analysis",
                "Compliance requirements",
                "Integration complexity",
                "Timeline constraints"
            ],
            "tools": ["Crypto discovery scanners", "Performance benchmarks", "Migration planners"]
        },
        
        "implementation_timeline": {
            "phase_1": "Assessment and planning (6-12 months)",
            "phase_2": "Hybrid deployment (12-24 months)", 
            "phase_3": "Full PQ migration (24-36 months)",
            "phase_4": "Classical algorithm deprecation (36+ months)"
        }
    }
    
    return migration_strategies