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In this paper we present two algorithms for the multiplication of sparse Laurent polynomials and Poisson series (the latter being algebraic structures commonly arising in Celestial Mechanics from the application of perturbation theories).…
We theoretically propose a symmetric encryption scheme based on Restricted Boltzmann Machines that functions as a probabilistic Enigma device, encoding information in the marginal distributions of visible states while utilizing bias…
We introduce an adaptable and modular hybrid architecture designed for fault-tolerant quantum computing. It combines quantum emitters and linear-optical entangling gates to leverage the strength of both matter-based and photonic-based…
The component-by-component construction is the standard method of finding good lattice rules or polynomial lattice rules for numerical integration. Several authors have reported that in numerical experiments the generating vector sometimes…
A lattice of integers is the collection of all linear combinations of a set of vectors for which all entries of the vectors are integers and all coefficients in the linear combinations are also integers. Lattice reduction refers to the…
Vector multiplication is a fundamental operation for AI acceleration, responsible for over 85% of computational load in convolution tasks. While essential, these operations are primary drivers of area, power, and delay in modern datapath…
In distributed matrix multiplication, a common scenario is to assign each worker a fraction of the multiplication task, by partitioning the input matrices into smaller submatrices. In particular, by dividing two input matrices into…
Multiplication is an indispensable operation in most of digital signal processing systems. Recently, many systems need to execute different types of algorithms on a multiplier. Therefore, it needs complicated computation and large area…
In a distributed computing system for the master-worker framework, an erasure code can mitigate the effects of slow workers, also called stragglers. The distributed computing system combined with coding is referred to as coded computation.…
As quantum computing technology continues to advance, post-quantum cryptographic methods capable of resisting quantum attacks have emerged as a critical area of focus. Given the potential vulnerability of existing homomorphic encryption…
This paper derives two new optimization-driven Monte Carlo algorithms inspired from variable splitting and data augmentation. In particular, the formulation of one of the proposed approaches is closely related to the alternating direction…
Differential Power Analysis (DPA) presents a major challenge to mathematically-secure cryptographic protocols. Attackers can break the encryption by measuring the energy consumed in the working digital circuit. To prevent this type of…
Integer forcing is an alternative approach to conventional linear receivers for multiple-antenna systems. In an integer-forcing receiver, integer linear combinations of messages are extracted from the received matrix before each individual…
Cryptographic primitives have been used for various non-cryptographic objectives, such as eliminating or reducing randomness and interaction. We show how to use cryptography to improve the time complexity of solving computational problems.…
Quantum samplers are believed capable of sampling efficiently from distributions that are classically hard to sample from. We consider a sampler inspired by the classical Ising model. It is nonadaptive and therefore experimentally amenable.…
Structured codes based on lattices were shown to provide enlarged capacity for multi-user communication networks. In this paper, we study capacity-approaching irregular repeat accumulate (IRA) codes over integer rings $\mathbb{Z}_{2^{m}}$…
We consider the problem of secure distributed matrix multiplication (SDMM) in which a user wishes to compute the product of two matrices with the assistance of honest but curious servers. We construct polynomial codes for SDMM by studying a…
Quadratic form reduction and lattice reduction are fundamental tools in computational number theory and in computer science, especially in cryptography. The celebrated Lenstra-Lenstra-Lov\'asz reduction algorithm (so-called LLL) has been…
We proposed a new attack against Hwang et al.'s cryptosystem. This cryptosystem uses a super-increasing sequence as private key and the authors investigate a new algorithm called permutation combination algorithm to enhance density of…
There is a recent trend in artificial intelligence (AI) inference towards lower precision data formats down to 8 bits and less. As multiplication is the most complex operation in typical inference tasks, there is a large demand for…