相关论文: A simple generalization of El-Gamal cryptosystem t…

In this article, we propose a method to construct self orthogonal matrix, orthogonal matrix and anti orthogonal matrix over the finite field. Orthogonal matrices has numerous applications in cryptography, so here we demonstrate the…

We propose variations of the class of hidden monomial cryptosystems in order to make it resistant to all known attacks. We use identities built upon a single bivariate polynomial equation with coefficients in a finite field. Indeed, it can…

We construct cryptographic trilinear maps that involve simple, non-ordinary abelian varieties over finite fields. In addition to the discrete logarithm problems on the abelian varieties, the cryptographic strength of the trilinear maps is…

Commutative encryption is a useful but rather strict notion in cryptography. In this paper, we deny a loose variation of commutative encryption-commutative-like encryption and give an example: the generalization of ElGamal scheme. The…

S. S. Magliveras et al. have described symmetric and public key cryptosystems based on logarithmic signatures (also known as group bases) for finite permutation groups. In this paper we show that if $G$ is a nontrivial finite group which is…

The El-Gamal AA_{\beta} Public Key Cryptosystem is a new asymmetric cryptosystem based on the piecewise AA_{\beta}-function. The AA_{\beta}-function which is essentially a one way Boolean function was motivated by the squaring and…

The article explores the creation of a cryptosystem using a halidon group ring of a dihedral group. Due to the non-abelian nature of the group, constructing the cryptosystem is more challenging compared to an abelian group. The logic used…

We present a study on the use of Pell hyperbolas in cryptosystems with security based on the discrete logarithm problem. Specifically, after introducing the group's structure over generalized Pell conics (and also giving the explicit…

The discrete logarithm problem is one of the backbones in public key cryptography. In this paper we study the discrete logarithm problem in the group of circulant matrices over a finite field. This gives rise to secure and fast public key…

We extend Rabin's cryptosystem to general number fields. We show that decryption of a random plaintext is as hard as the integer factorisation problem, provided the modulus in our scheme has been chosen carefully. We investigate the…

Let $f:X\to Y$ be a finite ramified Galois covering of algebraic varieties defined over the complex numbers. In this paper, we prove some structure theorems for such coverings in the case that the non-abelian Galois group of the cover is…

In this paper we generalize the definition of a multilinear map to arbitrary groups and develop a novel idea of multilinear cryptosystem using nilpotent group identities.

In this expository article we present an overview of the current state-of-the-art in post-quantum group-based cryptography. We describe several families of groups that have been proposed as platforms, with special emphasis in polycyclic…

This article introduces a novel cryptographic paradigm based on nonderived polyadic algebraic structures. Traditional cryptosystems rely on binary operations within groups, rings, or fields, whose well-understood properties can be exploited…

In this paper we consider cryptographic applications of the arithmetic on the hyperoctahedral group. On an appropriate subgroup of the latter, we particularly propose to construct public key cryptosystems based on the discrete logarithm.…

An improved design of a cryptosystem based on small Ree groups is proposed. We have changed the encryption algorithm and propose to use a logarithmic signature for the entire Ree group. This approach improves security against sequential key…

Cryptographic systems are derived using units in group rings. Combinations of types of units in group rings give units not of any particular type. This includes cases of taking powers of units and products of such powers and adds the…

A method for non-abelian Cramer-Shoup cryptosystem is presented. The role of decision and search is explored, and the platform of solvable/polycyclic group is suggested. In the process we review recent progress in non-abelian cryptography…

In this short note, we develop a novel idea of a bilinear cryptosystem using the discrete logarithm problem in matrices. These matrices come from a linear representation of a finite $p$-group of class 2. We discuss an example at the end.

Recently, Dor\"oz et al. (2017) proposed a new hard problem, called the finite field isomorphism problem, and constructed a fully homomorphic encryption scheme based on this problem. In this paper, we generalize the problem to the case of…