Related papers: Post-quantum hash functions using $\mathrm{SL}_n(\…

We present fast strongly universal string hashing families: they can process data at a rate of 0.2 CPU cycle per byte. Maybe surprisingly, we find that these families---though they require a large buffer of random numbers---are often faster…

This paper introduces a novel cryptographic approach based on the continuous logarithm in the complex circle, designed to address the challenges posed by quantum computing. By leveraging its multi-valued and spectral properties, this…

With the constantly advancing capabilities of quantum computers, conventional cryptographic systems relying on complex math problems may encounter unforeseen vulnerabilities. Unlike regular computers, which are often deemed cost-ineffective…

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.…

Nowadays, predominant asymmetric cryptographic schemes are considered to be secure because discrete logarithms are believed to be hard to be computed. The algorithm of Shor can effectively compute discrete logarithms, i.e. it can brake such…

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…

Diffie-Hellman key-agreement and RSA cryptosystem are widely used to provide security in internet protocols. But both of the two algorithms are totally breakable using Shor's algorithms. This paper proposes two connected matrix-based…

Separating hash families are useful combinatorial structures which are generalizations of many well-studied objects in combinatorics, cryptography and coding theory. In this paper, using tools from graph theory and additive number theory,…

Owing to their interesting spectral properties, the synthetic crystals over lattices other than regular Euclidean lattices, such as hyperbolic and fractal ones, have attracted renewed attention, especially from materials and meta-materials…

We introduce the Hidden Polynomial Function Graph Problem as a natural generalization of an abelian Hidden Subgroup Problem (HSP) where the subgroups and their cosets correspond to graphs of linear functions over the finite field F_p. For…

Advances in quantum computing make Shor's algorithm for factorising numbers ever more tractable. This threatens the security of any cryptographic system which often relies on the difficulty of factorisation. It also threatens methods based…

Binomial Cayley graphs are obtained by considering the binomial coefficient of the weight function of a given Cayley graph and a natural number. We introduce these objects and study two families: one associated with symmetric groups and the…

Post-quantum cryptography is essential for securing digital communications against threats posed by quantum computers. Re-searchers have focused on developing algorithms that can withstand attacks from both classical and quantum computers,…

The nonsemisimple quantum Cayley-Klein groups $ Fun(SU_{q}(2;\bf j}) $ are realized as Hopf algebra of the noncommutative functions with the dual (or Study) variables. The {\it dual} quantum algebras $ su_q(2;{\bf j}) $ are constructed and…

The results of computer searches for large graphs with given (small) degree and diameter are presented. The new graphs are Cayley graphs of semidirect products of cyclic groups and related groups. One fundamental use of our ``dense graphs''…

In this paper, we present a new construction for strong separating hash families by using hypergraphs and obtain some optimal separating hash families. We also improve some previously known bounds of separating hash families.

We study a family of harmonic univalent functions in the open unit disc defined by using post quantum calculus operators. We first obtained a coefficient characterization of these functions. Using this, coefficients estimates, distortion…

We propose a preimage attack against cryptographic hash functions based on the speedup enabled by quantum computing. Preimage resistance is a fundamental property cryptographic hash functions must possess. The motivation behind this work…

We present a construction of expander graphs obtained from Cayley graphs of narrow ray class groups, whose eigenvalue bounds follow from the Generalized Riemann Hypothesis. Our result implies that the Cayley graph of (Z/qZ)* with respect to…

We present a novel approach to post-quantum cryptography that employs directed-graph decryption of noise-enhanced high-memory convolutional codes. The proposed construction generates random-like generator matrices that effectively conceal…