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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 ]
NTRU is an open-source public-key cryptosystem that uses lattice-based cryptography to encrypt and decrypt data. It consists of two algorithms: NTRUEncrypt, which is used for encryption, and NTRUSign, which is used for digital signatures. Unlike other popular public-key cryptosystems, it is resistant to attacks using Shor's algorithm ...
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 ...
Another approach to signatures based on lattices over Rings is a variant of the patented NTRU family of lattice based cryptography. The primary example of this approach is a signature known as the Bimodal Lattice Signature Scheme (BLISS). It was developed by Ducas, Durmas, Lepoint and Lyubashevsky and documented in their paper "Lattice ...
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]
The references describe in full detail how this can be accomplished. It is more complicated than uniform sampling but it allows for a proof of security of the algorithm. The paper "Sampling from Discrete Gaussians for Lattice-Based Cryptography on a Constrained Device" by Dwarakanath and Galbraith provides an overview of this problem. [4]
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. He showed that it is secure in an average case if S V P γ {\displaystyle \mathrm {SVP} _{\gamma }} (where γ = n c {\displaystyle \gamma =n^{c}} for some constant c > 0 {\displaystyle c>0} ) is hard in ...
The method uses the Lenstra–Lenstra–Lovász lattice basis reduction algorithm (LLL) to find a polynomial that has the same zeroes as the target polynomial but smaller coefficients. In cryptography, the Coppersmith method is mainly used in attacks on RSA when parts of the secret key are known and forms a base for Coppersmith's attack.