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Lattice-based cryptography is the generic term for constructions of cryptographic primitives that involve lattices, either in the construction itself or in the security proof. Lattice-based constructions support important standards of post-quantum cryptography . [ 1 ]
Short integer solution (SIS) and ring-SIS problems are two average-case problems that are used in lattice-based cryptography constructions. Lattice-based cryptography began in 1996 from a seminal work by Miklós Ajtai [ 1 ] who presented a family of one-way functions based on SIS problem.
In computer science, lattice problems are a class of optimization problems related to mathematical objects called lattices.The conjectured intractability of such problems is central to the construction of secure lattice-based cryptosystems: lattice problems are an example of NP-hard problems which have been shown to be average-case hard, providing a test case for the security of cryptographic ...
IEEE P1363 is an Institute of Electrical and Electronics Engineers (IEEE) standardization project for public-key cryptography. It includes specifications for: Traditional public-key cryptography (IEEE Std 1363-2000 and 1363a-2004) Lattice-based public-key cryptography (IEEE Std 1363.1-2008) Password-based public-key cryptography (IEEE Std 1363. ...
[4] [5] Compared to competing PQ methods, it has typical advantages of lattice-based methods, e.g. in regard to runtime as well as the size of the ciphertexts and the key material. [ 6 ] Variants with different security levels have been defined: Kyber512 ( NIST security level 1, ≈ AES 128), Kyber768 (NIST security level 3, ≈AES 192), and ...
The Goldreich–Goldwasser–Halevi (GGH) lattice-based cryptosystem is a broken asymmetric cryptosystem based on lattices. There is also a GGH signature scheme which hasn't been broken as of 2024. The Goldreich–Goldwasser–Halevi (GGH) cryptosystem makes use of the fact that the closest vector problem can be a hard problem.
In cryptography, learning with errors (LWE) is a mathematical problem that is widely used to create secure encryption algorithms. [1] It is based on the idea of representing secret information as a set of equations with errors. In other words, LWE is a way to hide the value of a secret by introducing noise to it. [2]
In general terms, ideal lattices are lattices corresponding to ideals in rings of the form [] / for some irreducible polynomial of degree . [1] All of the definitions of ideal lattices from prior work are instances of the following general notion: let be a ring whose additive group is isomorphic to (i.e., it is a free -module of rank), and let be an additive isomorphism mapping to some lattice ...