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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
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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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Quantum Modular Multiplication
IEEE Access, 2020 Quantum modular multiplication circuit is one of the basic quantum computation circuits which are basic functions in quantum algorithms. However, since quantum-quantum modular multipliers require a high cost reversible modular inversion routine for ...
Seong-Min Cho +4 more
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A Modular Extension for a Computer Algebra System [PDF]
Programming and Computer Software, 2020 Computer algebra systems are complex software systems that cover a wide range of scientific and practical problems. However, the absolute coverage cannot be achieved. Often, it is required to create a user extension for an existing computer algebra system. In this case, the extensibility of the system should be taken into account.
Migran N. Gevorkyan +3 more
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Mathematics of Computation, 1961 It will be assumed that the reader is familiar w,ith the elementary theory of congruences [1]. Let in, M2, ... *, mn be s integers relatively prime in pairs and let Ml =MIM2 im8. Let xl, x2, * * , x8be an ordered set of s integers such that 0 < xi < mi.
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Modularity in Biological Evolution and Evolutionary Computation [PDF]
Biology Bulletin Reviews, 2020 The main text is in ...
Anton V. Eremeev, Alexander V. Spirov
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