Related papers: Cryptographic transformations over polyadic rings
This paper presents a novel post-quantum cryptosystem based on high-memory masked convolutional codes. Unlike conventional code-based schemes that rely on block codes with fixed dimensions and limited error-correction capability, our…
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 describe a new classical bit commitment protocol based on cryptographic constraints imposed by special relativity. The protocol is unconditionally secure against classical or quantum attacks. It evades the no-go results of Mayers, Lo and…
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…
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…
We develop matrix cryptography based on linear recurrent sequences of any order that allows securing encryption against brute force and chosen plaintext attacks. In particular, we solve the problem of generalizing error detection and…
We present in this paper an algorithm for exchanging session keys, coupled with a hashing encryption module. We show schemes designed for their potential invulnerability to classical and quantum attacks. In turn, if the parameters included…
Modifications of Markovski quasigroup based crypto-algorithm have been proposed. Some of these modifications are based on the systems of orthogonal n-ary groupoids. T-quasigroups based stream ciphers have been constructed.
The advent of quantum computing poses a significant threat to the foundational cryptographic algorithms that secure modern digital communications. Protocols such as HTTPS, digital certificates, and public key infrastructures (PKIs) heavily…
Akiyama et al. (Int. J. Math. Indust., 2019) proposed a post-quantum key exchange protocol that is based on the hardness of solving a system of multivariate non-linear polynomial equations but has a design strategy different from ordinary…
The Clifford hierarchy is a foundational concept for universal quantum computation (UQC). It was introduced to show that UQC can be realized via quantum teleportation, given access to certain standard resources. While the full structure of…
We give graphical characterisation of the access structure to both classical and quantum information encoded onto a multigraph defined for prime dimension $q$, as well as explicit decoding operations for quantum secret sharing based on…
Quantum money is the cryptographic application of the quantum no-cloning theorem. It has recently been instantiated by Montgomery and Sharif (Asiacrypt '24) from class group actions on elliptic curves. In this work, we propose a concrete…
Shor's quantum factoring algorithm and a few other efficient quantum algorithms break many classical crypto-systems. In response, people proposed post-quantum cryptography based on computational problems that are believed hard even for…
Chebyshev polynomials have been recently proposed for designing public-key systems. Indeed, they enjoy some nice chaotic properties, which seem to be suitable for use in Cryptography. Moreover, they satisfy a semi-group property, which…
We generalize the usual relationship between irreducible Zariski closed subsets of the affine space, their defining ideals, coordinate rings, and function fields, to a non-commutative setting, where "varieties" carry a PGL_n-action, regular…
Cryptography is the study of techniques for ensuring the secrecy and authentication of the information. Public-key encryption schemes are secure only if the authenticity of the public-key is assured. Elliptic curve arithmetic can be used to…
We consider representations of algebraic tori $T_n(F_q)$ over finite fields. We make use of normal elliptic bases to show that, for infinitely many squarefree integers $n$ and infinitely many values of $q$, we can encode $m$ torus elements,…
Sharing of notations and theories across an inheritance hierarchy of mathematical structures, e.g., groups and rings, is important for productivity when formalizing mathematics in proof assistants. The packed classes methodology is a…
We introduce cyclic diagram monoids, a generalisation of classical diagram monoids that adds elements of arbitrary period by including internal components, with a view towards cryptography. We classify their simple representations and…