Results 11 to 20 of about 74,008 (307)
An improved QFT-based quantum comparator and extended modular arithmetic using one ancilla qubit
New Journal of Physics, 2023 Quantum comparators and modular arithmetic are fundamental in many quantum algorithms. Current research mainly focuses on operations between two quantum states.
Yewei Yuan +6 more
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CoRR, 2023 We present a simple neural network that can learn modular arithmetic tasks and exhibits a sudden jump in generalization known as ``grokking''. Concretely, we present (i) fully-connected two-layer networks that exhibit grokking on various modular arithmetic tasks under vanilla gradient descent with the MSE loss function in the absence of any ...
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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 ...
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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
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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
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Modular realizations of hyperbolic Weyl groups [PDF]
, 2012 We study the recently discovered isomorphisms between hyperbolic Weyl groups and unfamiliar modular groups. These modular groups are defined over integer domains in normed division algebras, and we focus on the cases involving quaternions and octonions ...
Kleinschmidt, A. +2 more
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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
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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
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Hessian K3 surfaces of non-Sylvester type [PDF]
, 1995 We construct the moduli space of cubic surfaces which do not admit a Sylvester form as an arithmetic quotient, and determine the graded ring of modular forms of even ...
Nersessian, A., Ter-Antonian, V.M.
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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
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