Results 11 to 20 of about 21,194 (310)
Modular quantum computation in a trapped ion system
Nature Communications, 2019 Modern computation relies on modular architectures, breaking a complex algorithm into self-contained subroutines, whereas current quantum computers do not have such capability.
Kuan Zhang +9 more
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A modular reduction for GCD computation
Journal of Computational and Applied Mathematics, 2004 Most of integer GCD algorithms use one or several basic transformations which reduce at each step the size of the inputs integers u and v. These transformations called reductions are studied in a general framework.
Sedjelmaci, Sidi Mohammed
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Algorithmic Computation of Flattenings and of Modular Deformations
Journal of Symbolic Computation, 2002 This paper presents an algorithm for the computation of any jet of the flattening stratum of a module over a local algebra based on an obstruction theory for lifting flatness. It is applied to modular deformations of singular germs. Infinitesimal modular
Martin, Bernd
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Some Properties of the Computation of the Modular Inverse with Applications in Cryptography
Computation, 2023 In the field of cryptography, many algorithms rely on the computation of modular multiplicative inverses to ensure the security of their systems. In this study, we build upon our previous research by introducing a novel sequence, (zj)j≥0, that can ...
Michele Bufalo +2 more
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Computing Modular Polynomials [PDF]
LMS Journal of Computation and Mathematics, 2005 AbstractThis paper presents a new probabilistic algorithm to compute modular polynomials modulo a prime. Modular polynomials parameterize pairs of isogenous elliptic curves, and are useful in many aspects of computational number theory and cryptography. The algorithm presented here has the distinguishing feature that it does not involve the computation
Denis Xavier Charles, Kristin E. Lauter
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IEEE Access, 2022 Evolutionary computation techniques have always provided fascinating results in all the fields of science and engineering. However in the area of computer security, their contribution has been comparatively very less. More specifically if we consider the
Hridoy Jyoti Mahanta +4 more
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Transactions on Cryptographic Hardware and Embedded Systems, 2023 We propose a novel approach that generalizes interleaved modular multiplication algorithms for the computation of sums of products over large prime fields. This operation has widespread use and is at the core of many cryptographic applications.
Patrick Longa
doaj +1 more source
COMPUTING WITH SUBGROUPS OF THE MODULAR GROUP [PDF]
Glasgow Mathematical Journal, 2014 AbstractWe give several algorithms for finitely generated subgroups of the modular group PSL2(ℤ) given by sets of generators. First, we present an algorithm to check whether a finitely generated subgroup H has finite index in the full modular group. Then we discuss how to parametrise the right cosets of H in PSL2(ℤ), whether the index is finite or not.
Kirschmer, Markus +1 more
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Modular: The Super Computer [PDF]
, 2011 This article is deals with the history modular arithmetic, based on the rest classes calculus system «Restklassenarithmetik» (RCCS), or Modular Arithmetic, regarding its creation and development in the USSR. Characteristics of the USSR first modular super-computers: “Т-340А”, “К-340А”, “Diamond (Алмаз)” and “5E53” and their development history are ...
B. M. Malashevich, D. B. Malashevich
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