Results 1 to 10 of about 18,646 (160)
Montgomery Reduction for Gaussian Integers [PDF]
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
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Multiple color images security by SPN over the residue classes of Gaussian integer $$\:Z{\left[i\right]}_{h}$$ [PDF]
Scientific ReportsIn this paper, the authors present the design of a new pair of 8 × 8 S-boxes over the residue classes of Gaussian integers $$\:Z{\left[i\right]}_{h}$$ and their usage for the encryption of multiple RGB images using a three-stage Substitution-Permutation ...
Muhammad Sajjad +4 more
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Dimension of the intersection of certain Cantor sets in the plane [PDF]
Opuscula Mathematica, 2021 In this paper we consider a retained digits Cantor set \(T\) based on digit expansions with Gaussian integer base. Let \(F\) be the set all \(x\) such that the intersection of \(T\) with its translate by \(x\) is non-empty and let \(F_{\beta}\) be the ...
Steen Pedersen, Vincent T. Shaw
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IEEE Access, 2023 A code over Gaussian or Eisenstein integer residue ring is an additive group of vectors with entries in this integer residue ring which is closed under the action of constant multiplication by the Gaussian or Eisenstein integers. In this paper, we define
Hajime Matsui
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Gaussian Twin Neighborhood Prime Labeling on Fan Digraphs
Ratio Mathematica, 2023 Gaussian integers are complex numbers of the form \gamma=x+iy where x and y are integers and i^2=-1. The set of Gaussian integers is usually denoted by \mathbb{Z}[i].
K Palani, A Shunmugapriya
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Constant-time Implementation Method for Discrete Gaussian Sampling on Integer [PDF]
Jisuanji gongcheng, 2020 Discrete Gaussian sampling on integer is the basic operation implemented by lattice cryptosystems,and is also a determinant factor of security,but it may be subject to timing attacks and cause the leakage of secret information.To address the problem,this
LU Jiajia, DU Yusong
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Birth of optical vortices in propagating fields with an original fractional topological charge [PDF]
Компьютерная оптика, 2020 In contrast to the orbital angular momentum (OAM), which is conserved on free space propagation, the topological charge (TC) of a paraxial optical vortex (OV) is not conserved in the general case. Here, we investigate a Gaussian beam with a fractional TC
V.V. Kotlyar +2 more
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Formalized Mathematics, 2013 Summary Gaussian integer is one of basic algebraic integers. In this article we formalize some definitions about Gaussian integers [27]. We also formalize ring (called Gaussian integer ring), Z-module and Z-algebra generated by Gaussian integer mentioned above.
Yuichi Futa +3 more
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Estimate of the module of analogue Weyls trigonometrical sum in ring of Gaussian numbers [PDF]
Компьютерные исследования и моделирование, 2010 The ring of Gaussian numbers is considered. The estimation of the module of some analogue of Weyl's trigonometrical sum with summation on Gaussian numbers is proved by methods of the analytical number theory.
Pavel Nikolaevich Sorokin
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An asymmetric cryptography using Gaussian integers
Engineering and Applied Science Research, 2020 In this paper, the already strong McEliece cryptosystem is enhanced with atwo-dimensional finite Gaussian integer. By substituting the one-dimensional linear code with atwo-dimensional code employing afinite Gaussian integer, anew system ...
Wanarat Juraphanthong +1 more
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