Lattice-based cryptography was introduced in the mid 1990s in two different forms, independently by Ajtai-Dwork [AD97] and Hoffstein-Pipher-Silverman [HPSS08]. Thanks to the work of Stehlé-Steinfeld [SS11], we now understand the NTRU cryptosystem introduced by Hoffstein-Pipher-Silverman to be a variant of a cryptosystem which has security reductions to the Ring Learning With Errors (RLWE) probl...

In this paper, we introduce a method of threshold secret sharing scheme (TSSS) in which secret reconstruction is based on Babai's nearest plane algorithm. In order to supply secure public channels for transmitting shares to parties, we need to ensure that there are no quantum threats to these channels. A solution to this problem can be utilization of lattice-based cryptosystems for these channe...

Three-party Password Authenticated Key Exchange (3PAKE) protocol is an important cryptographic primitive, where clients can establish a session key using easy-to-remember passwords. A number of 3PAKE protocols based on traditional mathematical problems have been presented in the literature, but these protocols are not able to resist attacks using quantum computers. In this paper, we construct t...

Nearly all of the currently used and well-tested signature schemes (e.g. RSA or DSA) are based either on the factoring assumption or the presumed intractability of the discrete logarithm problem. Further algorithmic advances on these problems may lead to the unpleasant situation that a large number of schemes have to be replaced with alternatives. In this work we present such an alternative – a...

Authenticated key exchange (AKE) protocol is an important cryptographic primitive that assists communicating entities, who are communicating over an insecure network, to establish a shared session key to be used for protecting their subsequent communication. Lattice-based cryptographic primitives are believed to provide resilience against attacks from quantum computers. An efficient AKE protoco...

Residue Number Systems (RNS) are naturally considered as an interesting candidate to provide efficient arithmetic for implementations of cryptosystems such as RSA, ECC (Elliptic Curve Cryptography), pairings, etc. More recently, RNS have been used to accelerate fully homomorphic encryption as lattice-based cryptogaphy. In this paper, we present an RNS algorithm resolving the Closest Vector Prob...

Encryption and signature schemes based on worst-case lattice problems are promising candidates for the post-quantum era, where classic number-theoretic assumptions are rendered false. Although there have been many important results and breakthroughs in lattice cryptography, the questions of how to systematically evaluate their security in practice and how to choose secure parameters are still o...

Over the last years lattice-based cryptography has received much attention due to versatile average-case problems like Ring-LWE or Ring-SIS that appear to be intractable by quantum computers. But despite of promising constructions, only few results have been published on implementation issues on very constrained platforms. In this work we therefore study and compare implementations of Ring-LWE ...

In the innovative work secure communication and data protection are being main field, which emerged by cryptography as a fundamental pillar. Strong cryptographic methods now essential given rising reliance on digital technologies threats posed bad actors. This abstract examines evolution of protocols techniques it relates to advancements in cryptography. The development post-quantum is most not...

Non-Centered Discrete Gaussian sampling is a fundamental building block in many lattice-based constructions in cryptography, such as signature and identity-based encryption schemes. On the one hand, the center-dependent approaches, e.g. cumulative distribution tables (CDT), Knuth-Yao, the alias method, discrete Zigurat and their variants, are the fastest known algorithms to sample from a discre...