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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 ]
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 ...
The Short Integer Solution (SIS) problem is an average case problem that is used in lattice-based cryptography constructions. Lattice-based cryptography began in 1996 from a seminal work by Ajtai [ 1 ] who presented a family of one-way functions based on the SIS problem.
Computational hardness assumptions are of particular importance in cryptography. A major goal in cryptography is to create cryptographic primitives with provable security. In some cases, cryptographic protocols are found to have information theoretic security; the one-time pad is a common example. However, information theoretic security cannot ...
Post-quantum cryptography (PQC), sometimes referred to as quantum-proof, quantum-safe, or quantum-resistant, is the development of cryptographic algorithms (usually public-key algorithms) that are currently thought to be secure against a cryptanalytic attack by a quantum computer.
BLISS (short for Bimodal Lattice Signature Scheme) is a digital signature scheme proposed by Léo Ducas, Alain Durmus, Tancrède Lepoint and Vadim Lyubashevsky in their 2013 paper "Lattice Signature and Bimodal Gaussians".
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]
A major advantage that RLWE based cryptography has over the original learning with errors (LWE) based cryptography is found in the size of the public and private keys. RLWE keys are roughly the square root of keys in LWE. [1] For 128 bits of security an RLWE cryptographic algorithm would use public keys around 7000 bits in length. [9]