Results 1 to 10 of about 123 (98)
Optimization of the multivariate polynomial public key for quantum safe digital signature [PDF]
Scientific Reports, 2023 Kuang, Perepechaenko, and Barbeau recently proposed a novel quantum-safe digital signature algorithm called Multivariate Polynomial Public Key or MPPK/DS.
Randy Kuang, Maria Perepechaenko
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Counting monochromatic solutions to diagonal Diophantine equations
Discrete Analysis, 2021 Counting monochromatic solutions to diagonal Diophantine equations, Discrete Analysis 2021:14, 47 pp. An important subfield of Ramsey theory concerns questions of the following type: for which systems of equations $E_1,\dots,E_k$ in variables $x_1,\dots,
Sean Prendiville
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Quantitative results on Diophantine equations in many variables [PDF]
Acta Arithmetica, 2020 We consider a system of integer polynomials of the same degree with non-singular local zeros and in many variables. Generalising the work of Birch (1962) we find quantitative asymptotics (in terms of the maximum of the absolute value of the coefficients of these polynomials) for the number of integer zeros of this system within a growing box.
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On novel security systems based on the 2-cyclic refined integers and the foundations of 2-cyclic refined number theory [PDF]
Journal of Fuzzy Extension and ApplicationsIntegers play a basic role in the structures of asymmetric crypto-algorithms. Many famous public key crypto-schemes use the basics of number theory to share keys and decrypt and encrypt messages and multimedia.
Mohammad Abobala +2 more
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Diophantine equations in moderately many variables [PDF]
Michigan Mathematical Journal, 2016 We give upper bounds for the number of integral solutions of bounded height to a system of equations $f_i(x_1,\ldots,x_n) = 0$, $1 \leq i \leq r$, where the $f_i$ are polynomials with integer coefficients. The estimates are obtained by generalising an approach due to Heath-Brown, using a certain $q$-analogue of van der Corput's method, to the case of ...
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Diophantine equations in semiprimes
Discrete Analysis, 2019 Diophantine equations in semiprimes, Discrete Analysis 2019:17, 21 pp. This paper considers the problem of finding integer solutions to integral polynomial equations of the form $$f(x_1,\dots,x_n)=0\qquad\qquad (*)$$ with the condition that each ...
Shuntaro Yamagishi
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Another New Solvable Many-Body Model of Goldfish Type
Symmetry, Integrability and Geometry: Methods and Applications, 2012 A new solvable many-body problem is identified. It is characterized by nonlinear Newtonian equations of motion (''acceleration equal force'') featuring one-body and two-body velocity-dependent forces ''of goldfish type'' which determine the motion ofan ...
Francesco Calogero
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Counting integer points on affine surfaces with a side condition
Discrete AnalysisCounting integer points on affine surfaces with a side condition, Discrete Analysis 2025:12, 25 pp. This paper is concerned with special instances of the general problem of bounding the number of solutions to Diophantine equations with the variables ...
Tim Browning, Matteo Verzobio
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Diophantine equations in separated variables and polynomial power sums. [PDF]
Mon Hefte Math, 2021 Fuchs C, Heintze S.
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