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

Recently, additive combinatorics has blossomed into a vibrant area in mathematical sciences. But it seems to be a difficult area to define - perhaps because of a blend of ideas and techniques from several seemingly unrelated contexts which…

In this survey we describe a recently-developed technique for bounding the number (and controlling the typical structure) of finite objects with forbidden substructures. This technique exploits a subtle clustering phenomenon exhibited by…

In the last decade, a number of public key cryptosystems based on com- binatorial group theoretic problems in braid groups have been proposed. We survey these cryptosystems and some known attacks on them. This survey includes: Basic facts…

Affinely closed homogeneous spaces G/H, i.e., affine homogeneous spaces that admit only the trivial affine embedding, are characterized for any affine algebraic group G. As a corollary, a description of affine G-algebras with finitely…

Deep neural networks are vulnerable to a range of adversaries. A particularly pernicious class of vulnerabilities are backdoors, where model predictions diverge in the presence of subtle triggers in inputs. An attacker can implant a…

Despite the remarkable progress of diffusion models in image generation, recent studies reveal their vulnerability to backdoor attacks via covert visual or textual triggers. Although evolving defense mechanisms can detect most existing…

This article describes a lightweight additive homomorphic algorithm with the same encryption and decryption keys. Compared to standard additive homomorphic algorithms like Paillier, this algorithm reduces the computational cost of…

Secret sharing is an important building block in cryptography. All explicitly defined secret sharing schemes with known exact complexity bounds are multi-linear, thus are closely related to linear codes. The dual of such a linear scheme, in…

Several cryptographic protocols constructed based on less-known algorithmic problems, such as those in non-commutative groups, group rings, semigroups, etc., which claim quantum security, have been broken through classical reduction methods…

Edge devices in federated learning usually have much more limited computation and communication resources compared to servers in a data center. Recently, advanced model compression methods, like the Lottery Ticket Hypothesis, have already…

The discrete logarithm problem is one of the backbones in public key cryptography. In this paper we study the discrete logarithm problem in the group of circulant matrices over a finite field. This gives rise to secure and fast public key…

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.…

Architectural backdoors pose an under-examined but critical threat to deep neural networks, embedding malicious logic directly into a model's computational graph. Unlike traditional data poisoning or parameter manipulation, architectural…

The Hidden Subgroup Problem (HSP) is a computational problem which includes as special cases integer factorization, the discrete logarithm problem, graph isomorphism, and the shortest vector problem. The celebrated polynomial-time quantum…

Although homomorphic encryption can be incorporated into neural network layers for securing machine learning tasks, such as confidential inference over encrypted data samples and encrypted local models in federated learning, the…

An algebraic framework in which to study infinite sums is proposed, complementing and augmenting the usual topological tools. The framework subsumes numerous examples in the literature. It is developed using many varied examples, with a…

We investigate the theory of affine group schemes over a symmetric tensor category, with particular attention to the tangent space at the identity. We show that this carries the structure of a restricted Lie algebra, and can be viewed as…

Distributed state estimation arises in many applications such as position estimation in robot swarms, clock synchronization for processor networks, and data fusion. One characteristic is that agents only have access to noisy measurements of…

We employ tropical algebras as platforms for several cryptographic schemes that would be vulnerable to linear algebra attacks were they based on "usual" algebras as platforms.

We propose a new symmetric cryptographic scheme based on functional invariants defined over discrete oscillatory functions with hidden parameters. The scheme encodes a secret integer through a four-point algebraic identity preserved under…