latticebased

Lattice-based cryptography refers to a broad class of cryptographic constructions whose security is based on the presumed hardness of problems in lattice theory. A lattice is a discrete set of points in n-dimensional space with a regular geometric structure. The central idea is to design cryptographic primitives whose security reduces to difficult lattice problems, such as learning with errors (LWE), short vector problems (SVP), or closest vector problems (CVP), including their approximate and variant forms. These problems are believed to be resistant to attacks by quantum computers, making lattice-based schemes a leading candidate for post-quantum cryptography.

The most influential foundations are LWE and its variants, including Ring-LWE and Module-LWE, which enable efficient constructions by exploiting algebraic structures. Security reductions link the hardness of these average-case problems to the worst-case hardness of ideal lattice problems, providing a theoretical basis for security claims. Over time, lattice-based methods have yielded a diverse set of primitives, including public-key encryption, key exchange, digital signatures, and fully homomorphic encryption (FHE) schemes.

In practice, lattice-based schemes have evolved to address efficiency and scalability. Notable examples include schemes based on Ring-LWE or Module-LWE that underpin modern key exchange protocols and digital signatures. In recent years, lattice-based candidates have been standardized and standardized in post-quantum cryptography processes conducted by national and international bodies. Some well-known examples in contemporary use and standardization include algorithms for secure key exchange and signatures developed to meet performance and security requirements in a quantum-era setting. Ongoing research addresses parameter selection, side-channel resilience, and implementation optimizations.