Related papers: Cryptographic transformations over polyadic rings

We formalize the simulation paradigm of cryptography in terms of category theory and show that protocols secure against abstract attacks form a symmetric monoidal category, thus giving an abstract model of composable security definitions in…

The multistep solving strategy consists in a divide-and-conquer approach: when a multivariate polynomial system is computationally infeasible to solve directly, one variable is assigned over the elements of the base finite field, and the…

We propose a general security definition for cryptographic quantum protocols that implement classical non-reactive two-party tasks. The definition is expressed in terms of simple quantum-information-theoretic conditions which must be…

In this paper we present an attack on a recently proposed code-based Private Information Retrieval (PIR) scheme. Indeed, the server can retrieve the index of the desired file with high probability in polynomial time. The attack relies on…

In the realm of modern digital communication, cryptography, and signal processing, binary sequences with a low correlation properties play a pivotal role. In the literature, considerable efforts have been dedicated to constructing good…

The paper presents a comprehensive study of group codes from non-abelian split metacyclic group algebras. We derive an explicit Wedderburn-like decomposition of finite split metacyclic group algebras over fields with characteristic coprime…

We propose a symmetric key homomorphic encryption scheme based on the evaluation of multivariate polynomials over a finite field. The proposed scheme is somewhat homomorphic with respect to addition and multiplication. Further, we define a…

We present MMbeddings, a probabilistic embedding approach that reinterprets categorical embeddings through the lens of nonlinear mixed models, effectively bridging classical statistical theory with modern deep learning. By treating…

Process theories provide a powerful framework for describing compositional structures across diverse fields, from quantum mechanics to computational linguistics. Traditionally, they have been formalized using symmetric monoidal categories…

The theory of finite simple groups is a (rather unexplored) area likely to provide interesting computational problems and modelling tools useful in a cryptographic context. In this note, we review some applications of finite non-abelian…

Cryptography is the science of using mathematics to encrypt and decrypt data. Cryptography enables you to store sensitive information or transmit it across insecure networks so that it cannot be read by anyone except the intended recipient.…

We will construct post-quantum encryption algorithms based on three-variable polynomial Beal-Schur congruence. After giving a proof of Beal's conjecture and citing some applications of it to selected cases where the discrete logarithm and…

A symmetric encryption method based on properties of quasicrystals is proposed. The advantages of the cipher are strict aperiodicity and everywhere discontinuous property as well as the speed of computation, simplicity of implementation and…

Nowadays, using cryptographic systems play an effective role in security and safety technologies. One of the most applied kind of cryptography is Symmetric Cryptography and its applications. New aspects of symmetric Cryptography…

We initiate the study of multi-party computation for classical functionalities (in the plain model) with security against malicious polynomial-time quantum adversaries. We observe that existing techniques readily give a polynomial-round…

In this paper we study the MOR cryptosystem. We use the group of unitriangular matrices over a finite field as the non-abelian group in the MOR cryptosystem. We show that a cryptosystem similar to the El-Gamal cryptosystem over finite…

This paper deals with distributed matrix multiplication. Each player owns only one row of both matrices and wishes to learn about one distinct row of the product matrix, without revealing its input to the other players. We first improve on…

In this paper, we extend diagrammatic reasoning in monoidal categories with algebraic operations and equations. We achieve this by considering monoidal categories that are enriched in the category of Eilenberg-Moore algebras for a monad.…

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.

The advent of quantum computing poses a profound threat to traditional cryptographic systems, exposing vulnerabilities that compromise the security of digital communication channels reliant on RSA, ECC, and similar classical encryption…