Results 21 to 30 of about 575 (65)

Efficient computation of pairings on Jacobi quartic elliptic curves

Journal of Mathematical Cryptology, 2014
This paper proposes the computation of the Tate pairing, Ate pairing and its variations on the special Jacobi quartic elliptic curve Y2=dX4+Z4$Y^{2}=dX^{4}+Z^{4}$.
Duquesne Sylvain, El Mrabet Nadia, Fouotsa Emmanuel   +2 more
doaj   +1 more source

String Branchings on Complex Tori and Algebraic Representations of Generalized Krichever-Novikov Algebras

, 1992
The propagation differential for bosonic strings on a complex torus with three symmetric punctures is investigated. We study deformation aspects between two point and three point differentials as well as the behaviour of the corresponding Krichever ...
A. Hurwitz, Andreas Ruffing, H-y. Guo, H. E. Rauch, I. M. Krichever, L. Bonora, M. R. Bremner, M. Schlichenmaier, M. Schlichenmaier, M. Schlichenmaier, M. Schlichenmaier, Martin Schlichenmaier, R. Dick, Th. Deck, Thomas Deck   +14 more
core   +4 more sources

Noncommutative geometry of rational elliptic curves

, 2017
We study an interplay between operator algebras and geometry of rational elliptic curves. Namely, let $\mathcal{O}_B$ be the Cuntz-Krieger algebra given by square matrix $B=(b-1, ~1, ~b-2, ~1)$, where $b$ is an integer greater or equal to two.
Nikolaev, Igor
core   +1 more source

Character sums with division polynomials

, 2011
We obtain nontrivial estimates of quadratic character sums of division polynomials $\Psi_n(P)$, $n=1,2, ...$, evaluated at a given point $P$ on an elliptic curve over a finite field of $q$ elements.
Igor E. Shparlinski, Iwaniec, Katherine E. Stange, Kohel, Lauter, Shparlinski   +5 more
core   +1 more source

Distribution of Farey Fractions in Residue Classes and Lang--Trotter Conjectures on Average

, 2007
We prove that the set of Farey fractions of order $T$, that is, the set $\{\alpha/\beta \in \Q : \gcd(\alpha, \beta) = 1, 1 \le \alpha, \beta \le T\}$, is uniformly distributed in residue classes modulo a prime $p$ provided $T \ge p^{1/2 +\eps}$ for any ...
Cojocaru, A. C., Shparlinski, I. E.
core   +1 more source

Constructing elliptic curve isogenies in quantum subexponential time

Journal of Mathematical Cryptology, 2014
Given two ordinary elliptic curves over a finite field having the same cardinality and endomorphism ring, it is known that the curves admit a nonzero isogeny between them, but finding such an isogeny is believed to be computationally difficult.
Childs Andrew, Jao David, Soukharev Vladimir   +2 more
doaj   +1 more source

The 1729 K3 Surface

, 2016
We revisit the mathematics that Ramanujan developed in connection with the famous "taxi-cab" number $1729$. A study of his writings reveals that he had been studying Euler's diophantine equation $$ a^3+b^3=c^3+d^3.
Ono, Ken, Trebat-Leder, Sarah
core   +1 more source

Generating pairing-friendly elliptic curve parameters using sparse families

Journal of Mathematical Cryptology, 2018
The majority of methods for constructing pairing-friendly elliptic curves are based on representing the curve parameters as polynomial families. There are three such types, namely complete, complete with variable discriminant and sparse families. In this
Fotiadis Georgios, Konstantinou Elisavet
doaj   +1 more source

The dihedral hidden subgroup problem

Journal of Mathematical Cryptology
The hidden subgroup problem (HSP) is a cornerstone problem in quantum computing, which captures many problems of interest and provides a standard framework algorithm for their study based on Fourier sampling, one class of techniques known to provide ...
Chen Imin, Sun David
doaj   +1 more source

A new method of choosing primitive elements for Brezing–Weng families of pairing-friendly elliptic curves

Journal of Mathematical Cryptology, 2015
In this paper we present a new method of choosing primitive elements for Brezing–Weng families of pairing-friendly elliptic curves with small rho-values, and we improve on previously known best rho-values of families [J.
Yoon Kisoon
doaj   +1 more source