Results 31 to 40 of about 391,951 (282)
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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On primitive solutions of the Diophantine equation x2 + y2 = M
Open Mathematics, 2021 We provide explicit formulae for primitive, integral solutions to the Diophantine equation x2+y2=M{x}^{2}+{y}^{2}=M, where MM is a product of powers of Pythagorean primes, i.e., of primes of the form 4n+14n+1. It turns out that this is a nice application
Busenhart Chris +3 more
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Divisor problem in special sets of Gaussian integers
Karpatsʹkì Matematičnì Publìkacìï, 2016 Let $A_{1}$ and $A_{2}$ be fixed sets of gaussian integers. We denote by $\tau_{A_{1}, A_{2}}(\omega)$ the number of representations of $\omega$ in form $\omega=\alpha\beta$, where $\alpha \in A_{1}, \beta \in A_{2}$.
O.V. Savastru
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Construction and Decoding of BCH-Codes Over the Gaussian Field
IEEE Access, 2023 In this article, first we deliberate the theory of the Gaussian field and extension field of the Gaussian field. Secondly, we provide a comprehensive construction scheme for BCH codes over the Gaussian field.
Muhammad Sajjad +3 more
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The Diophantine equation ax2+2bxy−4ay2=±1
International Journal of Mathematics and Mathematical Sciences, 2003 We discuss, with the aid of arithmetical properties of the ring of the Gaussian integers, the solvability of the Diophantine equation ax2+2bxy−4ay2=±1, where a and b are nonnegative integers.
Lionel Bapoungué
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Preassigned character values in the Gaussian integers [PDF]
, 1970 Let γ1, γ2,…, γt be distinct prime Gaussian integers. With k an odd positive rational integer, take ω1, ω2,…, ωt to be k-th roots of unity, not necessarily distinct nor primitive.
Rabung, John R
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, 2021 . This memory is formed by three chapters. The first one contains some fundamental and common notions of any integral ring. The concepts related to Gaussian Integers as: units, Gaussian prime, greatest common divisor, factorization and unique ...
Remili, Liamine
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A quantum calculus framework for Gaussian Fibonacci and Gaussian Lucas quaternion numbers [PDF]
Notes on Number Theory and Discrete MathematicsIn order to investigate the relationship between Gaussian Fibonacci numbers and quantum numbers and to develop both a deeper theoretical understanding in this study, q-Gaussian Fibonacci, q-Gaussian Lucas quaternions and polynomials are taken with ...
Bahar Kuloğlu
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Solvability of certain exponential Lebesgue-Nagell equations 𝑥 2 + 𝑝 𝑚 = 𝑦 [PDF]
Songklanakarin Journal of Science and Technology (SJST), 2023 In this article, we first investigate the exponential Lebesgue-Nagell equation as shown in the title. Eventually, we can establish a necessary and sufficient criterion for having an integer solution to such an equation under the conditions that 𝑝 ≡ 3 ...
Patcharee Wongsason, Sawian Jaidee
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Montgomery Modular Arithmetic over Gaussian Integers
, 2020 The Montgomery multiplication is an efficient method for modular arithmetic. Typically, it is used for modular arithmetic over integer rings to prevent the expensive inversion for the modulo reduction.
Freudenberger, Jürgen +3 more
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