1 Summary of the review In this review I present the book " Post-Quantum Cryptography ". This volume gives a detailed, technical-level treatment of the post-quantum cryptography universe. 2 Summary of the book When (if?) quantum computers of a big enough size will be available, most of the current public-key cryptography primitives based on number theory will be vulnerable. The " next generatio...

The emergence of quantum computers threatens current cryptographic systems, and NIST is preparing for the post-quantum era through cryptography (PQC) contest. CRYSTALS-Kyber a lattice-based cipher suite that used as PQC standard. Lattice-based considered quantum-safe computing because algorithm can more efficiently solve lattice problem compared to classic has not been reported yet. In this pap...

The “Multivariate Ring Learning with Errors” problem was presented as a generalization of Errors (RLWE), introducing efficiency improvements respect to the RLWE counterpart thanks its multivariate structure. Nevertheless, recent attack by Bootland, Castryck and Vercauteren has some important consequences on security “non-coprime” cyclotomics; this transforms instances m-RLWE power-of-two cyclot...

Lattices have been used to construct many cryptographic primitives after Ajtai’s seminal paper in 1996. The goal of this paper is to design novel cryptographic primitives using lattices, which are still found to be no polynomial time attack by quantum computers. For achieving this, we survey the known lattice-based cryptography and lattice-based fully homomorphic encryption schemes as a first s...

We propose new multivariate cryptosystems over n-dimensional vector space over a finite field Fq based on idea of hidden discrete logarithm problem for F ∗ q. These cryptosystems are based on hidden eulerian equations x = a, (α, q − 1) = 1. The method is based on the idea of Eulerian transformations, which allow us to use asymmetric algorithms based on families of nonlinear multiplicatively inj...

knowledge, the same problems remain hard over arbitrary lattices, even with a quantum computer. More precisely, for certain sub-exponential approximation factors a, a-SVP on ideal lattices admit a polynomial-time algorithm, as depicted in Figure 1. In this survey, we give an overview of the techniques that have lead to these results. The first quantum attack on certain ideal lattices of cycloto...

Plantard T. , Rose M. and Willy S. (2009). Improvement of Lattice-based Cryptography using CRT. School of Computer and Software Engineering, University of Wollongong NSW, Australia. Ajtai, M. (1996). Generating Hard Instances of Lattice Problems. In Proceedings of the 28th annual ACM Symposium on Theory of Computing, New York, USA. Alese, B. K. (2000). Vulnerability Analysis of Encryption/Decry...

We continue the study of statistical zero-knowledge (SZK) proofs, both interactive and noninteractive, for computational problems on point lattices. We are particularly interested in the problem GapSPP of approximating the ε-smoothing parameter (for some ε < 1/2) of an n-dimensional lattice. The smoothing parameter is a key quantity in the study of lattices, and GapSPP has been emerging as a co...

In this paper, we report that we have solved the shortest vector problem (SVP) over a 128-dimensional lattice, which is currently the highest dimension of the SVP that has ever been solved. The security of lattice-based cryptography is based on the hardness of solving the SVP in lattices. In 2010 Micciancio et al. proposed a Gauss Sieve algorithm for heuristically solving the SVP using list L o...