Related papers: Group ring cryptography
In this paper a secret sharing scheme based on the word problem in groups is introduced. The security of the scheme and possible variations are discussed in section 2. The article concludes with the suggestion of two categories of platform…
Some geometry on non-singular cubic curves, mainly over finite fields, is surveyed. Such a curve has 9,3,1 or 0 points of inflexion, and cubic curves are classified accordingly. The group structure and the possible numbers of rational…
In this paper, algorithms for multivariate public key cryptography and digital signature are described. Plain messages and encrypted messages are arrays, consisting of elements from a fixed finite ring or field. The encryption and…
Let $f=(f_0,f_1,\dots, f_{\nu-1})$ be a collection of one-to-one functions from some space~$X$ into itself such that the sets $f_j(X)$ are disjoint. If $w=w_1w_2\cdots w_k$ is a word on the alphabet $\{0,1,\dots,\nu-1\}$, let $\Phi_{f,w} =…
The remarkably long-standing problem of cryptography is to generate completely secure key. It is widely believed that the task cannot be achieved within classical cryptography. However, there is no proof in support of this belief. We…
Graded rings provide a natural algebraic framework for encoding symmetry via decompositions into homogeneous components indexed by a group, together with multiplication rules reflecting the group operation. Among graded rings, strongly…
Ring signature is a kind of group-oriented signature. It allows a member of a group to sign messages on behalf of the group without revealing his/her identity. Certificateless public key cryptography was first introduced by Al-Riyami and…
In this paper we will give various examples of exponentially distorted subgroups in linear groups, including some new example of subgroups of $SL_n(\mathbb{Z}[x])$ for $n \ge 3$, and show how they can be used to construct symmetric-key…
A new scheme of probabilistic subgroup-related encryption is introduced. Some applications of this scheme based on the RSA, Diffie-Hellman and ElGamal encryption algorithms are described. Security assumptions and main advantages of this…
Complex information-processing systems, for example quantum circuits, cryptographic protocols, or multi-player games, are naturally described as networks composed of more basic information-processing systems. A modular analysis of such…
For commutative rings, we introduce the notion of a {\em universal grading}, which can be viewed as the "largest possible grading". While not every commutative ring (or order) has a universal grading, we prove that every {\em reduced order}…
The goal of any cryptographic system is the exchange of information among the intended users without any leakage of information to others who may have unauthorized access to it. A common secret key could be created over a public channel…
We develop cryptographically secure techniques to guarantee unconditional privacy for respondents to polls. Our constructions are efficient and practical, and are shown not to allow cheating respondents to affect the ``tally'' by more than…
In this paper I consider all possible properties from commutative algebra for polynomial composites and monoid domains. The aim is full characterization of these structures. I start with the examination of group, ring, modules properties,…
The emergence of small computing devices and the integration of processing units into everyday objects has made lightweight cryptography an essential part of the security landscape. Conventional cryptographic algorithms such as AES, RSA,…
Any secured system can be modeled as a capability-based access control system in which each user is given a set of secret keys of the resources he is granted access to. In some large systems with resource-constrained devices, such as sensor…
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.
The theory of Engel groups plays an important role in group theory since these groups are closely related to the Burnside problems. In this survey we consider several classical and novel algorithmic problems for Engel groups and propose…
In this paper, an algorithm is aimed to make a cryptosystem for gray level images based on voice features, secret sharing scheme and electromagnetic rotor machine. Here, Shamir secret sharing (k n) threshold scheme is used to secure a key…
Quantum-mechanical devices have the potential to transform cryptography. Most research in this area has focused either on the information-theoretic advantages of quantum protocols or on the security of classical cryptographic schemes…