Related papers: On Hidden Sums Compatible with A Given Block Ciphe…
Using a finite geometric framework for studying the pentagon and heptagon codes we show that the concepts of quantum secret sharing and contextuality can be studied in a nice and unified manner. The basic idea is a careful study of the…
A cluster algebra is a commutative algebra whose structure is decided by a skew-symmetrizable matrix or a quiver. When a skew-symmetrizable matrix is invariant under an action of a finite group and this action is admissible, the folded…
In this paper, we investigate the computational complexity of the knapsack problem and subset sum problem for the following tropical algebraic structures. We consider the semigroup of square matrices of size $k \times k$ with non-negative…
Most cryptosystems are defined over finite algebraic structures where arithmetic operations are performed modulo natural numbers. This applies to private key as well as to public key ciphers. No secure cryptosystems defined over the field…
Secret sharing provides a means to distribute shares of a secret such that any authorized subset of shares, specified by an access structure, can be pooled together to recompute the secret. The standard secret sharing model requires public…
We propose a new homomorphic encryption scheme based on the hardness of decoding under independent random noise from certain affine families of codes. Unlike in previous lattice-based homomorphic encryption schemes, where the message is…
Federated Learning (FL) has emerged as a popular paradigm for collaborative learning among multiple parties. It is considered privacy-friendly because local data remains on personal devices, and only intermediate parameters -- such as…
We describe an efficient quantum algorithm for computing discrete logarithms in semigroups using Shor's algorithms for period finding and discrete log as subroutines. Thus proposed cryptosystems based on the presumed hardness of discrete…
In this paper, we introduce and develop the circle embedding method. This method hinges essentially on a combinatorial-geometric structure which we choose to call circles of partition. We provide applications in the context of problems that…
An average-case variant of the $k$-SUM conjecture asserts that finding $k$ numbers that sum to 0 in a list of $r$ random numbers, each of the order $r^k$, cannot be done in much less than $r^{\lceil k/2 \rceil}$ time. On the other hand, in…
We present a new group law defined on a subset of the projective plane $\mathbb{F}P^2$ over an arbitrary field $\mathbb{F}$, which lends itself to applications in Public Key Cryptography, in particular to a Diffie-Hellman-like key agreement…
A subalgebra pair of semisimple complex algebras B < A with inclusion matrix M is depth two if MM^t M < nM for some positive integer n and all corresponding entries. If A and B are the group algebras of finite group-subgroup pair H < G, the…
Irregular pyramids are made of a stack of successively reduced graphs embedded in the plane. Such pyramids are used within the segmentation framework to encode a hierarchy of partitions. The different graph models used within the irregular…
We introduce the notion of a Lie algebroid structure on an affine bundle whose base manifold is fibred over the real numbers. It is argued that this is the framework which one needs for coming to a time-dependent generalization of the…
Subspace clustering is an important problem in machine learning with many applications in computer vision and pattern recognition. Prior work has studied this problem using algebraic, iterative, statistical, low-rank and sparse…
Without assuming the field structure on the additive group of real numbers $\mathbb{R}$ with the usual order $<,$ we explore the fact that every proper subgroup of $\mathbb{R}$ is either closed or dense. This property of subgroups of the…
Maximally embedding dimension (MED) numerical semigroups are a wide and interesting family, with some remarkable algebraic and combinatorial properties. Associated to any numerical semigroup one can construct a MED closure, as it is well…
In this paper, we show that coherent sets of gambles and coherent lower and upper previsions can be embedded into the algebraic structure of information algebra. This leads firstly, to a new perspective of the algebraic and logical…
Using a quiver algebra of a cyclic quiver, we construct a faithful categorical action of the extended braid group of affine type A on its bounded homotopy category of finitely generated projective modules. The algebra is trigraded and we…
We propose a new randomized ensemble technique with a provable security guarantee against black-box transfer attacks. Our proof constructs a new security problem for random binary classifiers which is easier to empirically verify and a…