A cryptographically-relevant quantum computer would break the public-key cryptography that secures the internet: Shor's algorithm factors integers and solves discrete logarithms in polynomial time, defeating RSA, Diffie–Hellman and ECC. Post-quantum cryptography is the family of classical algorithms whose security rests on problems believed hard for both classical and quantum machines.
Working principle
The NIST-standardised front-runners are lattice-based. Their hardness comes from the Module Learning-With-Errors (MLWE) problem: recovering a secret vector from many noisy linear equations modulo q. Adding small random errors makes the system intractable, yet a party holding the secret can still decrypt or verify efficiently. FIPS 203 (ML-KEM, formerly Kyber) is a key-encapsulation mechanism; FIPS 204 (ML-DSA, formerly Dilithium) is a digital-signature scheme.
| Standard | Algorithm | Family | Use |
|---|---|---|---|
| FIPS 203 | ML-KEM (Kyber) | Module-lattice | Key establishment |
| FIPS 204 | ML-DSA (Dilithium) | Module-lattice | Signatures |
| FIPS 205 | SLH-DSA (SPHINCS+) | Hash-based | Stateless signatures |
| Draft | FN-DSA (Falcon) | Lattice (NTRU) | Compact signatures |
Migration and hybrid mode
Because the new schemes are young, deployments use hybrid key exchange — running ML-KEM alongside X25519 so the session stays secure if either holds. TLS 1.3 and SSH already ship hybrid groups. The driving concern is “harvest now, decrypt later”: adversaries record encrypted traffic today to decrypt once quantum hardware matures.
Trade-offLattice schemes trade larger keys and ciphertexts (kilobytes vs. tens of bytes) for quantum resistance — a real bandwidth and latency cost on constrained links.
Applications
- TLS, VPN and messaging key exchange (hybrid X25519+ML-KEM)
- Firmware and software signing with hash-based SLH-DSA
- Long-lived secrets: government, financial and medical archives
References & further reading
- NIST FIPS 203/204/205, Post-Quantum Cryptography Standards, 2024.
- Bos et al., “CRYSTALS-Kyber: a CCA-secure module-lattice-based KEM,” 2018.
- Shor, “Algorithms for quantum computation: discrete logarithms and factoring,” 1994.