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We introduce a new combinatorial structure: the superselector. We show that superselectors subsume several important combinatorial structures used in the past few years to solve problems in group testing, compressed sensing, multi-channel…
Recently, several cryptosystems have been proposed based semidirect products of various algebraic structures. Efficient attacks against several of them have already been given, along with a very general attack. The purpose of this note is…
An obfuscator is an algorithm that translates circuits into functionally-equivalent similarly-sized circuits that are hard to understand. Efficient obfuscators would have many applications in cryptography. Until recently, theoretical…
Secure codes are widely-studied combinatorial structures which were introduced for traitor tracing in broadcast encryption. To determine the maximum size of such structures is the main research objective. In this paper, we investigate the…
An overview of quantum computing and in particular the Hidden Subgroup Problem are presented from a mathematical viewpoint. Detailed proofs are supplied for many important results from the literature, and notation is unified, making it…
Using the tensor category theory developed by Lepowsky, Zhang and the second author, we construct a braided tensor category structure with a twist on a semisimple category of modules for an affine Lie algebra at an admissible level. We…
Eavesdropping attacks in inference systems aim to learn not the raw data, but the system inferences to predict and manipulate system actions. We argue that conventional information security measures can be ambiguous on the adversary's…
Let $\Gamma$ be a finite subgroup of $\SL_2(\C)$. We consider $\Gamma$-fixed point sets in Hilbert schemes of points on the affine plane $\C^2$. The direct sum of homology groups of components has a structure of a representation of the…
Scattering diagrams arose in the context of mirror symmetry, but a special class of scattering diagrams (the cluster scattering diagrams) were recently developed to prove key structural results on cluster algebras. We use the connection to…
Attack vectors that compromise machine learning pipelines in the physical world have been demonstrated in recent research, from perturbations to architectural components. Building on this work, we illustrate the self-obfuscation attack:…
We discuss a new attack, termed a dimension or linear decomposition attack, on several known group-based cryptosystems. This attack gives a polynomial time deterministic algorithm that recovers the secret shared key from the public data in…
We obfuscate words of a given length in a free monoid on two generators with a simple factorization algorithm (namely $SL_2(\mathbb{N})$) to create a public-key encryption scheme. We provide a reference implementation in Python and…
We introduce a new attack paradigm that embeds hidden adversarial capabilities directly into diffusion models via fine-tuning, without altering their observable behavior or requiring modifications during inference. Unlike prior approaches…
Substitution boxes with thorough cryptographic strengths are essential for the development of strong encryption systems. They are the only portions capable of inducing nonlinearity in symmetric encryption systems. Bijective substitution…
In the present paper, we study a purely inseparable counterpart of Abhyankar's conjecture for the affine line in positive characteristic, and prove its validity for all the finite local non-abelian simple group schemes in characteristic…
We provide algorithms for performing computations in generalized numerical semigroups, that is, submonoids of $\mathbb{N}^{d}$ with finite complement in $\mathbb{N}^{d}$. These semigroups are affine semigroups, which in particular implies…
Federated clustering allows multiple parties to discover patterns in distributed data without sharing raw samples. To reduce overhead, many protocols disclose intermediate centroids during training. While often treated as harmless for…
In this paper, we consider a question of sum-keeping about a multiplicative subsemigroup and its generator subsets in a semiring, and develop some elementary (collapse) process of the sum-keeping retraction through subsets until one minimal…
We address a cryptanalysis of two protocols based on the supposed difficulty of discrete logarithm problem on (semi) groups of matrices over a group ring. We can find the secret key and break entirely the protocols.
A group code structure of a linear code is a description of the code as one-sided or two-sided ideal of a group algebra of a finite group. In these realizations, the group algebra is identified with the ambient space, and the group elements…