Modern lattice-based cryptosystems require sampling from discrete Gaussian distributions. We review lattice based schemes and collect their requirements for sampling from discrete Gaussians. Then we survey the algorithms implementing such sampling and assess their practical performance. Finally we draw some conclusions regarding the best candidates for implementation on different platforms in t...

This article presets a review of the achievements rapidly developing field of cryptography - public-key cryptography based on the lattice theory. Paper contains the necessary basic concepts and the major problems of the lattice theory, as well as together with the description on the benefits of this cryptography class - the properties of the reliability to quantum computers and full homomorphis...

This article presets a review of lattice lattice basis reduction types. Paper contains the main five types of lattice basis reduction: size reduced (weak Hermit), c-reduced, Lovasz condition, Hermit-Korkin-Zolotarev, Minkowski reduced. The article provides references to applications in: information theory (decoding of coding group in MIMO), calculus (minimize of the positive quadratic form), co...

Lattice-based cryptography is one of the leading proposals for post-quantum cryptography. The Shortest Vector Problem (SVP) arguably most important problem cryptanalysis lattice-based cryptography, and many schemes have security claims based on its hardness. best quantum algorithm SVP due to Laarhoven [] runs in (heuristic) time \(2^{0.2653d + o(d)}\). In this article, we present an improvement...

We describe a general technique to simplify as well as to improve several lattice based cryptographic protocols. The technique is rather straightforward and is easily applied to the protocols, and gives both a simpler analysis and better performance than the original protocols. The improvement is global: the modiied protocols are simpler, faster, require less storage, use less bandwidth and nee...

Lattice based cryptography is gaining more and more importance in the cryptographic community. It is a common approach to use a special class of lattices, so-called ideal lattices, as the basis of lattice based crypto systems. This speeds up computations and saves storage space for cryptographic keys. The most important underlying hard problem is the shortest vector problem. So far there is no ...

With the development of quantum computing, existing cryptography schemes based on classical cryptographic primitives will no longer be secure. Hence, cryptographers are designing post-quantum (PQC) schemes, and ideal lattice-based has emerged as a prime candidate. Today, becomes more mature, its performance an important optimization goal. In cryptography, polynomial arithmetic sampling most tim...