Results 21 to 30 of about 549 (46)
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 +2 more
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Edwards Curves and Gaussian Hypergeometric Series [PDF]
, 2015 Let $E$ be an elliptic curve described by either an Edwards model or a twisted Edwards model over $\mathbb{F}_p$, namely, $E$ is defined by one of the following equations $x^2+y^2=a^2(1+x^2y^2),\, a^5-a\not\equiv 0$ mod $p$, or, $ax^2+y^2=1+dx^2y^2,\,ad ...
El-Sissi, Nermine, Sadek, Mohammad
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Tight closure and plus closure for cones over elliptic curves [PDF]
, 2005 We characterize the tight closure of graded primary ideals in a homogeneous coordinate ring over an elliptic curve by numerical conditions and we show that it is in positive characteristic the same as the plus closure.Comment: Some minor ...
Brenner, Holger
core +2 more sources
, 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 +14 more
core +4 more sources
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 +2 more
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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
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, 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
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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
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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 +5 more
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COMPUTING IMAGES OF GALOIS REPRESENTATIONS ATTACHED TO ELLIPTIC CURVES
Forum of Mathematics, Sigma, 2016 Let $E$ be an elliptic curve without complex multiplication (CM) over a number field $K$
ANDREW V. SUTHERLAND
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