Clear DefinitionsLattice-based Cryptography
1 min read
Pronunciation
[lat-is beyst krip-tog-ruh-fee]
Analogy
Imagine a vast, perfectly regular grid of points (a lattice) in a very high-dimensional space. Lattice-based cryptography is like hiding a secret by picking a point on this grid that's very close to another, randomly chosen, public point *off* the grid. It's easy to pick such a nearby grid point if you know the secret structure of the grid. But for someone else, even knowing the public off-grid point, finding your secret nearby grid point is like finding a specific grain of sand on an enormous, complex beach – very hard, even for quantum computers.
Definition
A type of public-key cryptography that uses mathematical structures called lattices. It is a leading candidate for post-quantum cryptography (PQC) because the underlying hard problems are believed to be resistant to attacks by both classical and quantum computers.
Key Points Intro
Lattice-based cryptography offers promising security against future quantum computers.
Key Points
Based on computationally hard problems on lattices, such as the Shortest Vector Problem (SVP) and Learning With Errors (LWE).
Considered a strong candidate for post-quantum cryptography (PQC) standards.
Can be used for encryption, digital signatures, and more advanced schemes like fully homomorphic encryption.
Generally offers strong security guarantees based on worst-case hardness assumptions.
Example
Several algorithms selected or considered by NIST for PQC standardization, such as CRYSTALS-Kyber (for key encapsulation) and CRYSTALS-Dilithium (for digital signatures), are based on lattice problems.
Technical Deep Dive
Lattices are discrete subgroups of R^n, essentially regularly arranged sets of points. Hard problems on lattices include finding the shortest non-zero vector in a lattice (SVP), finding the closest lattice vector to a given target vector (CVP), and solving the Learning With Errors (LWE) problem. The LWE problem involves distinguishing noisy linear equations from random ones, and its hardness is related to worst-case lattice problems. Lattice-based schemes often have relatively fast computations but can have larger key sizes or ciphertexts compared to traditional ECC or RSA for similar classical security levels.
Security Warning
While lattice-based cryptography is a leading PQC candidate, it's a relatively newer field compared to RSA or ECC. Ongoing research continues to refine algorithms and analyze their security. Parameter selection is critical, and implementations must be carefully vetted.
Lattice-based Cryptography - Related Articles
No related articles for this term.