Post-Quantum Cryptography - Dr. Nikhil Kumar Rajput

Understanding the Quantum Threat

🔍 Shor's Algorithm Impact

Shor's algorithm can efficiently factor large integers and solve discrete logarithm problems, breaking RSA, ECDSA, and Diffie-Hellman key exchange.

Polynomial time factoring
Breaks 2048-bit RSA in hours
Compromises elliptic curve cryptography
Threatens PKI infrastructure

⚡ Grover's Algorithm

Grover's algorithm provides quadratic speedup for unstructured search, effectively halving the security level of symmetric cryptographic primitives.

Square root speedup for search
AES-128 → 64-bit security
SHA-256 → 128-bit security
Requires doubling key sizes

📊 Timeline Assessment

Current estimates suggest cryptographically relevant quantum computers may emerge within 10-15 years, requiring immediate preparation.

NISQ era: 50-1000 qubits
Fault-tolerant QC: 2030-2035
Cryptographic relevance: 2035-2040
Y2Q (Years to Quantum) countdown

🎯 Attack Scenarios

Various attack models including "harvest now, decrypt later" where encrypted data is stored today for future quantum decryption.

Store-now-decrypt-later attacks
Retroactive cryptanalysis
Long-lived sensitive data
Forward security requirements

PQC Migration Timeline

2016

NIST PQC Standardization Begins

NIST announces post-quantum cryptography standardization process.

2022

First Standards Released

NIST publishes FIPS 203 (Kyber), FIPS 204 (Dilithium), FIPS 205 (SPHINCS+).

2024

Industry Adoption Phase

Major vendors begin implementing PQC algorithms in products and services.

2025-2030

Hybrid Transition Period

Dual-use classical and post-quantum algorithms for backward compatibility.

2030-2035

Full PQC Migration

Complete transition to post-quantum cryptography across all systems.

2035+

Quantum-Safe Era

Cryptographically relevant quantum computers emerge; PQC provides protection.

Implementation Examples

CRYSTALS-Kyber Key Generation

# Using pqcrypto library for Kyber
from pqcrypto.kem.kyber512 import generate_keypair, encrypt, decrypt
import os

# Generate key pair
public_key, secret_key = generate_keypair()

print(f"Public key size: {len(public_key)} bytes")
print(f"Secret key size: {len(secret_key)} bytes")

# Key encapsulation
ciphertext, shared_secret = encrypt(public_key)

print(f"Ciphertext size: {len(ciphertext)} bytes")
print(f"Shared secret: {shared_secret.hex()}")

# Key decapsulation
decrypted_secret = decrypt(secret_key, ciphertext)

# Verify shared secrets match
assert shared_secret == decrypted_secret
print("✅ Key exchange successful!")

CRYSTALS-Dilithium Digital Signatures

# Dilithium digital signature example
from pqcrypto.sign.dilithium2 import generate_keypair, sign, verify

# Generate signing key pair
public_key, secret_key = generate_keypair()

# Message to sign
message = b"This is a post-quantum secure message"

# Create digital signature
signature = sign(secret_key, message)

print(f"Message: {message.decode()}")
print(f"Signature size: {len(signature)} bytes")

# Verify signature
try:
    verify(public_key, message, signature)
    print("✅ Signature verification successful!")
except:
    print("❌ Signature verification failed!")

# Demonstrate security
tampered_message = b"This is a tampered message"
try:
    verify(public_key, tampered_message, signature)
    print("❌ This should not happen!")
except:
    print("✅ Tampered message correctly rejected")

Hybrid Classical-PQC Implementation

# Hybrid approach using both RSA and Kyber
from cryptography.hazmat.primitives.asymmetric import rsa
from cryptography.hazmat.primitives import hashes, serialization
from pqcrypto.kem.kyber512 import generate_keypair as kyber_keygen
from pqcrypto.kem.kyber512 import encrypt as kyber_encrypt
import os

class HybridKEM:
    def __init__(self):
        # Generate RSA key pair (classical)
        self.rsa_private = rsa.generate_private_key(
            public_exponent=65537,
            key_size=2048
        )
        self.rsa_public = self.rsa_private.public_key()
        
        # Generate Kyber key pair (post-quantum)
        self.kyber_public, self.kyber_private = kyber_keygen()
    
    def encapsulate(self):
        """Hybrid key encapsulation using both RSA and Kyber"""
        # Classical component
        rsa_secret = os.urandom(32)
        rsa_ciphertext = self.rsa_public.encrypt(
            rsa_secret,
            padding.OAEP(
                mgf=padding.MGF1(algorithm=hashes.SHA256()),
                algorithm=hashes.SHA256(),
                label=None
            )
        )
        
        # Post-quantum component
        kyber_ciphertext, kyber_secret = kyber_encrypt(self.kyber_public)
        
        # Combine secrets using KDF
        combined_secret = hashes.Hash(hashes.SHA256())
        combined_secret.update(rsa_secret)
        combined_secret.update(kyber_secret)
        final_secret = combined_secret.finalize()
        
        return {
            'rsa_ct': rsa_ciphertext,
            'kyber_ct': kyber_ciphertext,
            'secret': final_secret
        }

# Usage example
hybrid_kem = HybridKEM()
result = hybrid_kem.encapsulate()
print(f"Hybrid shared secret: {result['secret'].hex()}")
print("✅ Secure against both classical and quantum attacks!")

Standards & Compliance

🏛️ NIST Standards

FIPS 203 - Kyber Key Encapsulation APPROVED

Module-lattice-based key encapsulation mechanism for secure key exchange.

FIPS 204 - Dilithium Digital Signatures APPROVED

Lattice-based digital signature standard for authentication and non-repudiation.

FIPS 205 - SPHINCS+ Hash-based Signatures APPROVED

Stateless hash-based signature scheme with strong security guarantees.

🌍 International Standards

ISO/IEC 23837 - PQC Standards IN PROGRESS

International standard for post-quantum cryptographic algorithms.

ETSI QSC - Quantum-Safe Cryptography DEVELOPING

European technical specifications for quantum-safe implementations.

BSI TR-02102 - Cryptographic Mechanisms UPDATED

German Federal Office guidelines for post-quantum cryptography.

🔐 Post-Quantum Cryptography