Post-Quantum Cryptography

Post-quantum cryptography fundamentals

Post-quantum cryptography (PQC) develops cryptographic algorithms designed to remain secure against sufficiently powerful quantum computers. Quantum computers running Shor’s algorithm could efficiently solve the integer-factorization, discrete-logarithm, and elliptic-curve discrete-logarithm problems underlying RSA, Diffie–Hellman, and elliptic-curve cryptography. Although current quantum computers cannot yet break these systems, organizations must begin migration because sensitive data captured today could be decrypted later. Mosca’s theorem provides a framework for assessing the urgency of this transition. PQC research focuses mainly on lattice-based, code-based, hash-based, multivariate, and isogeny-based cryptography. Lattice-based schemes such as ML-KEM (Kyber) and ML-DSA (Dilithium) were among NIST’s first finalized standards in 2024, while hash-based signatures provide conservative security based on well-studied hash functions. In contrast, symmetric cryptography and hash functions are comparatively resistant to quantum attacks: Grover’s algorithm provides only a quadratic speedup, which can generally be mitigated by increasing key sizes, such as using 256-bit symmetric keys for approximately 128-bit post-quantum security. PQC algorithms often involve trade-offs, including larger keys, ciphertexts, signatures, or computational costs, and migration planning should also preserve properties such as forward secrecy.

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Quantum threats to public-key cryptography

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