Lattice-Based Cryptography

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Lattice-based cryptography is a type of post-quantum cryptography that relies on the mathematical properties of lattices to create secure encryption and other cryptographic primitives.

• believed to be resistant to quantum computers
• leverages the difficulty of solving certain problems on lattices
  • e.g., Shortest Vector Problem (SVP) and Closest Vector Problem (CVP)
  • involve finding specific vectors within the lattice based on certain criteria

A lattice is a structured arrangement of points in space, defined by a set of linearly independent vectors called a basis.

• i.e. a grid of dots in multiple dimensions, where each dot can be reached by combining the basis vectors with integer scaling
• higher dimensional lattices are used in cryptography

Features and Benefits

• post-quantum security
• efficiency and scalability
• homomorphic encryption
  • type of encryption that allows computations to be performed on encrypted data without decrypting it
• privacy-preserving cryptography
  • lattice-based cryptography is being explored in privacy-preserving applications such as zero-knowledge proofs

CRYSTALS-Dilithium

CRYSTALS-Dliithium is a lattice-based digital signature algorithm designed to be resistant to attacks from quantum computers.

• now called ML-DSA
• part of CRYSTALS (Cryptographic Suite for Algebraic Lattices) family
• intended to replace older signature schemes
  • i.e. RSA and ECC
• is a general-purpose digital signature scheme
  • can be used in a variety of applications

Features and Benefits

• lattice-based cryptography
• post-quantum cryptography
• digital signature scheme
  • can verify the authenticity and integrity of digital messages
• NIST Standard
  • standardized in 2024