Results 21 to 30 of about 74,008 (307)
Minimizing CNOT-count in quantum circuit of the extended Shor’s algorithm for ECDLP
Cybersecurity, 2023 The elliptic curve discrete logarithm problem (ECDLP) is a popular choice for cryptosystems due to its high level of security. However, with the advent of the extended Shor’s algorithm, there is concern that ECDLP may soon be vulnerable.
Xia Liu, Huan Yang, Li Yang
doaj +1 more source
Implementation of RSA Signatures on GPU and CPU Architectures
IEEE Access, 2020 This paper reports a constant-time CPU and GPU software implementation of the RSA exponentiation by using algorithms that offer a first-line defense against timing and cache attacks.
Eduardo Ochoa-Jimenez +3 more
doaj +1 more source
Hardware acceleration of number theoretic transform for zk‐SNARK
Engineering Reports, EarlyView., 2023 An FPGA‐based hardware accelerator with a multi‐level pipeline is designed to support the large‐bitwidth and large‐scale NTT tasks in zk‐SNARK. It can be flexibly scaled to different scales of FPGAs and has been equipped in the heterogeneous acceleration system with the help of HLS and OpenCL.
Haixu Zhao +6 more
wiley +1 more source
Segment LLL Reduction of Lattice Bases Using Modular Arithmetic
Algorithms, 2010 The algorithm of Lenstra, Lenstra, and Lovász (LLL) transforms a given integer lattice basis into a reduced basis. Storjohann improved the worst case complexity of LLL algorithms by a factor of O(n) using modular arithmetic.
Sanjay Mehrotra, Zhifeng Li
doaj +1 more source
Montgomery Reduction for Gaussian Integers
Cryptography, 2021 Modular arithmetic over integers is required for many cryptography systems. Montgomery reduction is an efficient algorithm for the modulo reduction after a multiplication. Typically, Montgomery reduction is used for rings of ordinary integers.
Malek Safieh, Jürgen Freudenberger
doaj +1 more source
Algorithms for estimating modular numbers in floating-point arithmetic
Наука. Инновации. Технологии, 2022 In the residue number system (RNS), the operations of addition, subtraction, and multiplication are executed in parallel for different digits (residues) of the modular numbers.
Konstantin Sergeevich Isupov
doaj
Bio-Inspired Constant-Time Arithmetic Kernels in Hybrid Membrane–Neural Spiking P Systems
MathematicsThis work introduces Hybrid Membrane–Neural P systems (HMN P systems), a computational model that integrates principles from membrane computing and spiking neural P systems. The resulting framework offers a versatile foundation for the development of bio-
Eduardo Vázquez +7 more
doaj +1 more source
A Modular Framework for Generic Quantum Algorithms
Mathematics, 2022 We describe a general-purpose framework to design quantum algorithms. This framework relies on two pillars: a basic data structure called quantum matrix and a modular structure based on three quasi-independent modules.
Alberto Manzano +6 more
doaj +1 more source
On classification of modular categories by rank
, 2016 The feasibility of a classification-by-rank program for modular categories follows from the Rank-Finiteness Theorem. We develop arithmetic, representation theoretic and algebraic methods for classifying modular categories by rank.
Burns +7 more
core +1 more source
A generating function of the squares of Legendre polynomials
, 2012 We relate a one-parametric generating function for the squares of Legendre polynomials to an arithmetic hypergeometric series whose parametrisation by a level 7 modular function was recently given by Shaun Cooper. By using this modular parametrisation we
Zudilin, Wadim
core +1 more source