Post-quantum public-key encryption: what’s it all about?
a day ago
- Public-key cryptography basics: RSA uses prime numbers p, q; public key n=pq; encryption involves modular exponentiation; security relies on factoring difficulty.
- Post-quantum (PQ) cryptography is needed due to potential quantum computers breaking RSA and Diffie-Hellman; new systems are less understood.
- Author presents a toy PQ cryptosystem using vectors, matrices, and modular arithmetic to illustrate structure; it's not secure for real use.
- Toy system: private key = two small vectors (a0, a1); public key = A = a0 + T*a1 where T is random matrix; encryption adds noise via dot products.
- Decryption in toy system recovers message plus noise; decryption can fail due to noise accumulation, a feature shared by many real PQ systems.
- Real PQ systems (e.g., FrodoKEM, ML-KEM, HQC) follow similar additive structure but differ in algebraic spaces, parameter sizes, and noise handling.
- Other systems (BIKE, NTRU Prime) use multiplicative inversion; Classic McEliece uses error-correcting codes with huge public keys but no decryption failures.
- Security considerations: attackers face hard search problem among many plausible vectors; defenses include non-interactive proofs and seed-based key generation.
- Classic McEliece is the most conservative option but has large public keys; other systems balance efficiency and security.