Lattice-Based Cryptography Reference
Reference 为 lattice-based cryptographic primitives including LWE, SIS, 和 NTRU schemes.
Hard Problems
The Learning With Errors (LWE) problem asks to recover a secret vector from noisy linear equations. Short Integer Solution (SIS) asks to find a short nonzero vector in a kernel lattice. Both reduce to worst-case lattice problems like GapSVP and SIVP, giving strong security foundations. The ring and module variants improve efficiency while maintaining security under structured assumptions.
- LWE
- Noisy linear equations
- SIS
- Short kernel vector
- Ring-LWE
- Polynomial ring variant
Regev 2005Ajtai 1996efficientSchemes and Security
Lattice-based KEMs like Kyber (ML-KEM) provide IND-CCA2 security via the Fujisaki-Okamoto transform. Lattice-based signatures like Dilithium (ML-DSA) use the Fiat-Shamir abstraction with aborts. NTRU offers an alternative lattice-based KEM with a long security history. All these schemes are believed resistant to quantum attacks, motivating their NIST standardization.
- Kyber/ML-KEM
- Lattice KEM
- Dilithium/ML-DSA
- Lattice signature
- NTRU
- Polynomial ring KEM
NIST standardFiat-Shamirlong history