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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 ]
Given a polynomial t(x) find small polynomials f 1 (x) and f 2 (x) such that: a(x)·f 1 (x) + f 2 (x) = t(x) If this problem is difficult to solve, then the signature scheme will be difficult to forge. [See the Wikipedia article on Ring Learning with Errors or Ideal Lattice Cryptography for more details on the theoretical difficulty of this ...
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 ...
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. He showed that it is secure in an average case if the shortest vector problem S V P γ {\displaystyle \mathrm {SVP} _{\gamma }} (where γ = n c {\displaystyle \gamma =n^{c}} for some constant c > 0 ...
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 ...
An important feature of basing cryptography on the ring learning with errors problem is the fact that the solution to the RLWE problem can be used to solve a version of the shortest vector problem (SVP) in a lattice (a polynomial-time reduction from this SVP problem to the RLWE problem has been presented [1]).
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.
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. ...