Related papers: On some quasigroup cryptographical primitives
We propose a new homomorphic public-key cryptosystem over arbitrary nonidentity finite group based on the difficulty of the membership problem for groups of integer matrices. Besides, a homomorphic cryptosystem is designed for the first…
We propose a cryptosystem based on matrices over group rings and claim that it is secure against adaptive chosen ciphertext attack.
We introduce a new type of cryptographic primitive that we call hiding fingerprinting. A (quantum) fingerprinting scheme translates a binary string of length $n$ to $d$ (qu)bits, typically $d\ll n$, such that given any string $y$ and a…
This paper classifies quasiprimitive permutation groups with a transitive subgroup which is isomorphic to $\A_n$ for some $n\geqslant5$.
We develop a generalized framework for invariant-based cryptography by extending the use of structural identities as core cryptographic mechanisms. Starting from a previously introduced scheme where a secret is encoded via a four-point…
Artin's braid groups have been recently suggested as a new source for public-key cryptography. In this paper we propose the first group signature schemes based on the conjugacy problem, decomposition problem and root problem in the braid…
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…
In this paper we review and comment on "A novel protocol-authentication algorithm ruling out a man-in-the-middle attack in quantum cryptography", [M. Peev et al., Int. J. Quant. Inform., 3, 225, (2005)]. In particular, we point out that the…
This paper investigates the use of quasigroups, Hadamard transforms and Number Theoretic Transforms for use in sequence randomization. This can also be used to generate hash functions for sequence encryption.
Braid group is a very important non-commutative group. It is also an important tool of quantum field theory, and has good topological properties. This paper focuses on the provable security research of cryptosystem over braid group, which…
We define a translation based cipher over an arbitrary finite field, and study the permutation group generated by the round functions of such a cipher. We show that under certain cryptographic assumptions this group is primitive. Moreover,…
Recently, several cryptosystems have been proposed based semidirect products of various algebraic structures. Efficient attacks against several of them have already been given, along with a very general attack. The purpose of this note is…
A quasi-semiregular element in a permutation group is an element that has a unique fixed point and acts semiregularly on the remaining points. Such elements were first studied in the context of automorphisms of graphs and occur naturally in…
Various descending chains of subgroups of a finite permutation group can be used to define a sequence of `basic' permutation groups that are analogues of composition factors for abstract finite groups. Primitive groups have been the…
A During last two decades, there has been a prolific growth in the chaos based image encryption algorithms. Up to an extent these algorithms have been able to provide an alternative to exchange large media files (images and videos) over the…
Presentations of racks is studied and a cryptographic protocol defined on racks is proposed.
The first contribution of the paper is to put forward an abstract definition of the Grain family of stream ciphers which formalises the different components that are required to specify a particular member of the family. Our second…
Secret sharing schemes based on the idea of hidden multipliers in encryption are proposed. As a platform, one can use both multiplicative groups of finite fields and groups of invertible elements of commutative rings, in particular,…
We introduce the quasi-ordinarization transform of a numerical semigroup. This transform will allow to organize all the semigroups of a given genus in a forest rooted at all quasi-ordinary semigroups with the given genus. This construction…
By resorting to basic features of topological knot theory we propose a (classical) cryptographic protocol based on the `difficulty' of decomposing complex knots generated as connected sums of prime knots and their mutants. The scheme…