Related papers: On Hidden Sums Compatible with A Given Block Ciphe…

Most heavy computation occurs on servers owned by a second party. This reduces data privacy, resulting in interest in data-oblivious computation, which typically severely degrades performance. Secure and fast delegated computation is…

Multivariate Cryptography is one of the candidates for Post-quantum Cryptography. Multivariate schemes are usually constructed by applying two secret affine invertible transformations $\mathcal S,\mathcal T$ to a set of multivariate…

Ideas from Fourier analysis have been used in cryptography for the last three decades. Akavia, Goldwasser and Safra unified some of these ideas to give a complete algorithm that finds significant Fourier coefficients of functions on any…

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…

We prove a characterization of profinite algebras, i.e., topological algebras that are isomorphic to a projective limit of finite discrete algebras. In general profiniteness concerns both the topological and algebraic characteristics of a…

We investigate the cryptanalysis of affine ciphers using a hybrid neural network architecture that combines modular arithmetic-aware and statistical feature-based learning. Inspired by recent advances in interpretable neural networks for…

Recent advances in federated learning have demonstrated its promising capability to learn on decentralized datasets. However, a considerable amount of work has raised concerns due to the potential risks of adversaries participating in the…

In this paper we study numerical semigroups containing a given positive integer and closed with respect to the action of an affine map. For such semigroups we find a minimal set of generators, their embedding dimension, their genus and…

The notion of hidden symmetry algebra used in the context of exactly solvable systems is re-examined from the purely algebraic way, analyzing subspaces of commuting polynomials that generate finite-dimensional quadratic algebras. By…

The first part of the paper is a brief overview of Hindman's finite sums theorem, its prehistory and a few of its further generalizations, and a modern technique used in proving these and similar results, which is based on idempotent…

Quantum algorithms for factoring and discrete logarithm have previously been generalized to finding hidden subgroups of finite Abelian groups. This paper explores the possibility of extending this general viewpoint to finding hidden…

In the field of algorithmic analysis, one of the more well-known exercises is the subset sum problem. That is, given a set of integers, determine whether one or more integers in the set can sum to a target value. Aside from the brute-force…

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…

As ML models become increasingly complex and integral to high-stakes domains such as finance and healthcare, they also become more susceptible to sophisticated adversarial attacks. We investigate the threat posed by undetectable backdoors,…

In a backdoor attack on a machine learning model, an adversary produces a model that performs well on normal inputs but outputs targeted misclassifications on inputs containing a small trigger pattern. Model compression is a widely-used…

Federated learning enables thousands of participants to construct a deep learning model without sharing their private training data with each other. For example, multiple smartphones can jointly train a next-word predictor for keyboards…

We establish an algorithm to encrypt and decrypt messages, where messages can be seen as elements of a finite field, using of mutations in a cluster algebra finite type.

Using well-known mathematical problems for encryption is a widely used technique because they are computationally hard and provide security against potential attacks on the encryption method. The subset sum problem (SSP) can be defined as…

In this paper we will first introduce the notion of affine structures on a ringed space and then obtain several properties. Affine structures on a ringed space, arising mainly from complex analytical spaces of algebraic schemes over number…

We provide a survey on the Hidden Subgroup Problem (HSP), which plays an important role in studying the security of public-key cryptosystems. We first review the abelian case, where Kitaev's algorithm yields an efficient quantum solution to…