Results 1 to 10 of about 128 (95)
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
doaj +2 more sources
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
Finite Sets with Large Algebraic Closures in Nilpotent Groups
Sultan Qaboos University Journal for ScienceAlgebraic sets play a central role in algebraic geometry over groups; by definition, an algebraic set is the set of common roots of a collection of equations in some non-commuting variables x1, ..., xn having coefficients in some group G.
Omar Al Raisi, Mohammad Shahryari
doaj +1 more source
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
doaj +1 more source
Communications on Pure and Applied Mathematics, Volume 79, Issue 9, Page 2107-2157, September 2026.ABSTRACT The leading‐order asymptotic behavior of the solution of the Cauchy initial‐value problem for the Benjamin–Ono equation in L2(R)$L^2(\mathbb {R})$ is obtained explicitly for generic rational initial data u0$u_0$. An explicit asymptotic wave profile uZD(t,x;ε)$u^\mathrm{ZD}(t,x;\epsilon)$ is given, in terms of the branches of the multivalued ...
Elliot Blackstone +3 more
wiley +1 more source
On 7‐adic Galois representations for elliptic curves over Q$\mathbb {Q}$
Proceedings of the London Mathematical Society, Volume 133, Issue 2, August 2026.Abstract In recent years, significant progress has been made on Mazur's Program B, with many authors beginning a systematic classification of all possible images of p$p$‐adic Galois representations attached to elliptic curves over Q$\mathbb {Q}$. Currently, the classification is only complete for p∈{2,3,13,17}$p \in \lbrace 2,3,13,17\rbrace$.
Lorenzo Furio, Davide Lombardo
wiley +1 more source
Fourier Expansion‐Based Approach to the Parameter Space of Classical Systems
Annalen der Physik, Volume 538, Issue 7, July 2026.ABSTRACT We propose a new approach to compute the classical metric tensor (CMT) and the Hannay curvature using Fourier series expansions in action‐angle variables. This approach circumvents the need for complex time‐domain integrals or the construction of generating functions, replacing them with algebraic combinations of Fourier coefficients. We prove
Marcos J. Hernández +3 more
wiley +1 more source
On the moments of exponential sums over r$r$‐free polynomials
Bulletin of the London Mathematical Society, Volume 58, Issue 7, July 2026.Abstract Let Fq[t]${\mathbb {F}}_q[t]$ denote the ring of polynomials over the finite field Fq${\mathbb {F}}_q$. Building off of techniques of Balog and Ruzsa and of Keil in the integer setting, we determine the precise order of magnitude of k$k$th moments of exponential sums over r$r$‐free polynomials in Fq[t]${\mathbb {F}}_q[t]$ for all k>0$k>0$.
Ben Doyle
wiley +1 more source