Related papers: Bilinear cryptography using finite $p$-groups of n…

We present a systematic approach to the construction of Miura transformations for discrete Painlev\'e equations. Our method is based on the bilinear formalism and we start with the expression of the nonlinear discrete equation in terms of…

Lightweight cryptography is a key tool for building strong security solutions for pervasive devices with limited resources. Due to the stringent cost constraints inherent in extremely large applications (ranging from RFIDs and smart cards…

In the recently emerging field of group-based cryptography, the Conjugacy Search Problem (CSP) has gained traction as a non-commutative replacement of the Discrete Log Problem (DLP). The problem of finding a secure class of nonabelian…

At CRYPTO 2017, Bela\"id et al presented two new private multiplication algorithms over finite fields, to be used in secure masking schemes. To date, these algorithms have the lowest known complexity in terms of bilinear multiplication and…

We discuss a new attack, termed a dimension or linear decomposition attack, on several known group-based cryptosystems. This attack gives a polynomial time deterministic algorithm that recovers the secret shared key from the public data in…

This paper introduces a novel approach to algebraic multigrid methods for large systems of linear equations coming from finite element discretizations of certain elliptic second order partial differential equations. Based on a discrete…

A class of two-bit bit flipping algorithms for decoding low-density parity-check codes over the binary symmetric channel was proposed in [1]. Initial results showed that decoders which employ a group of these algorithms operating in…

Let $1<g_1<\ldots<g_{\varphi(p-1)}<p-1$ be the ordered primitive roots modulo~$p$. We study the pseudorandomness of the binary sequence $(s_n)$ defined by $s_n\equiv g_{n+1}+g_{n+2}\bmod 2$, $n=0,1,\ldots$. In particular, we study the…

Witness encryption using multilinear maps was first proposed in 2013, and has continued to evolve since. In this paper, we build on an open-source multilinear map implementation by Carmer and Malozemoff of the graded encoding scheme CLT13…

We use the structure of finite-dimensional graded algebras to develop the theory of antilinear representations of finite $C_2$-graded groups. A finite $C_2$-graded group is a finite group with a subgroup of index 2. In this theory the…

In this paper we study the MOR cryptosystem using finite classical Chevalley groups over a finite field of odd characteristic. In the process we develop an algorithm for these Chevalley groups in the same spirit as the row-column operation…

We discuss a matrix public key cryptosystem and its numerical implementation.

In this paper, for an odd prime $p$, several classes of two-weight linear codes over the finite field $\mathbb{F}_p$ are constructed from the defining sets, and then their complete weight distributions are determined by employing character…

The new class of integrable mappings and chains is introduced. Corresponding (1+2) integrable systems invariant with respect to such discrete transformations are represented in explicit form. Soliton like solutions of them are represented…

Bilinear systems emerge in a wide variety of fields as natural models for dynamical systems ranging from robotics to quantum dots. Analyzing controllability of such systems is of fundamental and practical importance, for example, for the…

Bilinear systems of equations are defined, motivated and analyzed for solvability. Elementary structure is mentioned and it is shown that all solutions may be obtained as rank one completions of a linear matrix polynomial derived from…

We construct uncountably categorical 3-nilpotent groups of exponent p > 3. They are not one-based and do not allow the interpretation of an infinite field. Therefore they are counterexamples to Zilbers Conjecture. First 2-nilpotent new…

Recent breakthrough methods \cite{gggz,joux,bgjt} on computing discrete logarithms in small characteristic finite fields share an interesting feature in common with the earlier medium prime function field sieve method \cite{jl}. To solve…

Several cryptographic protocols constructed based on less-known algorithmic problems, such as those in non-commutative groups, group rings, semigroups, etc., which claim quantum security, have been broken through classical reduction methods…

We propose new provable practical deterministic polynomial time algorithm for the braid Wang, Xu, Li, Lin and Wang Double shielded public key cryptosystems. We show that a linear decomposition attack based on the decomposition method…