Results 21 to 30 of about 3,554 (146)
Modular Integer Arithmetic [PDF]
Formalized Mathematics, 2008 In this article we show the correctness of integer arithmetic based on Chinese Remainder theorem as described e.g. in [11]: Integers are transformed to finite sequences of modular integers, on which the arithmetic operations are performed. Retransformation of the results to the integers is then accomplished by means of the Chinese Remainder theorem ...
openaire +1 more source
Balancing act: Multivariate rational reconstruction for IBP
Nuclear Physics B, 2023 We address the problem of unambiguous reconstruction of rational functions of many variables. This is particularly relevant for recovery of exact expansion coefficients in integration-by-parts identites (IBPs) based on modular arithmetic.
A.V. Belitsky +2 more
doaj +1 more source
Computation of Odd Magic Square Using a New Approach with Some Properties [PDF]
Engineering and Technology Journal, 2012 Several aspects of magic square studies fall within the computations all universes. Experimented computation has reverted patterns, some of which have lead to analytic insight.
Shatha A. Al-Najjar +2 more
doaj +1 more source
Наука. Инновации. Технологии, 2022 The traditional way of building modular devices constructive postulates the need to include in the modular device bulky non-modular unit that is running a series-parallel op-erations of modular arithmetic.
Viljan Mavlutinovich Amerbaev +3 more
doaj
Method to Improve the Cryptographic Properties of S-Boxes
IEEE Access, 2023 This study presents a method based on elementary logic and arithmetic operations to enhance the cryptographic properties of Substitution Boxes (S-Boxes).
Jesus Agustin Aboytes-Gonzalez +4 more
doaj +1 more source
Masta: An HE-Friendly Cipher Using Modular Arithmetic
IEEE Access, 2020 The Rasta cipher, proposed by Dobraunig et al. (CRYPTO 2018), is an HE-friendly cipher enjoying the fewest ANDs per bit and the lowest ANDdepth among the existing ciphers.
Jincheol Ha +6 more
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
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
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