Lattice-Based Cryptography
Definition
Lattice-based cryptography is a family of cryptographic constructions whose security relies on the difficulty of solving mathematical problems involving lattices—regular arrangements of points in high-dimensional space. Most NIST post-quantum standards (Kyber, Dilithium, FALCON) use lattice-based approaches.
Technical Explanation
A lattice is a discrete set of points in n-dimensional space forming a regular grid pattern. Hard lattice problems include: Shortest Vector Problem (SVP)—finding the shortest non-zero vector, Closest Vector Problem (CVP)—finding the lattice point nearest to a target, and Learning With Errors (LWE)—distinguishing noisy linear equations from random.
No known quantum algorithm efficiently solves these problems. The best quantum speedup is the square root improvement from Grover's algorithm, which parameter selection easily compensates. Structured variants (Ring-LWE, Module-LWE) enable practical key sizes and performance.
SynX Relevance
SynX's Kyber-768 implementation uses Module-LWE lattice cryptography for key encapsulation. This provides efficient, well-studied post-quantum security for all key exchange operations. Combined with hash-based SPHINCS+ signatures, SynX achieves defense-in-depth across different mathematical foundations.
Frequently Asked Questions
- Why are lattices quantum-resistant?
- No known quantum algorithm efficiently solves hard lattice problems; Shor's algorithm doesn't apply.
- How long have lattices been studied?
- Lattice problems have been researched since the 1980s, with cryptographic applications since the 1990s.
- Are all lattice schemes the same?
- No—different constructions (NTRU, Ring-LWE, Module-LWE) have varying properties and security assumptions.
Lattice-based protection for your assets. Experience SynX security