Results 11 to 20 of about 2,144,780 (355)
Murmurations of Elliptic Curves [PDF]
Experimental Mathematics, 2022 We investigate the average value of the Frobenius trace at p over elliptic curves in a fixed conductor range with given rank. Plotting this average as p varies over the primes yields a striking oscillating pattern, the details of which vary with the rank.
Yang-Hui He +3 more
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Security analysis of elliptic curves with embedding degree 1 proposed in PLOS ONE 2016. [PDF]
PLoS ONE, 2019 Wang et al. proposed a method for obtaining elliptic curves with embedding degree 1 for securing critical infrastructures, and presented several elliptic curves generated by their method with torsion points of 160 bits and 189 bits orders.
Tadanori Teruya
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On Pythagorean elliptic curves [PDF]
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1994 For a primitive Pythagorean triple \((a,b,c)\) with \(a\) even, let \(E= E(a,b,c)\) be the elliptic curve \(y^ 2= x(x- a^ 2)(x- c^ 2)\). The author gives necessary and sufficient conditions for \(E/\mathbb{Q}\) to have non-zero rank. Said conditions are expressed in terms of the existence of non-zero solutions to a system of two diophantine equations ...
Norio Adachi
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Journal of Geometry and Physics, 1995 A detailed study is made of super elliptic curves, namely super Riemann surfaces of genus one considered as algebraic varieties, particularly their relation with their Picard groups. This is the simplest setting in which to study the geometric consequences of the fact that certain cohomology groups of super Riemann surfaces are not freely generated ...
Jeffrey M. Rabin
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COMPUTING IMAGES OF GALOIS REPRESENTATIONS ATTACHED TO ELLIPTIC CURVES [PDF]
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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On hashing into elliptic curves [PDF]
Journal of Mathematical Cryptology, 2009 We study the hash function from a finite field 𝔽q into an elliptic curve over 𝔽q which has recently been introduced by T. Icart. In particular we slightly adjust and prove the asymptotic formula conjectured by T. Icart for the image size of this function.
Farashahi Reza R. +2 more
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Cryptographically Strong Elliptic Curves of Prime Order [PDF]
International Journal of Electronics and Telecommunications, 2021 The purpose of this paper is to generate cryptographically strong elliptic curves over prime fields Fp, where p is a Mersenne prime, one of the special primes or a random prime. We search for elliptic curves which orders are also prime numbers.
Marcin Barański +2 more
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The review on elliptic curves as cryptographic pairing groups [PDF]
Mathematics and Computational Sciences, 2021 Elliptic curve is a set of two variable points on polynomials of degree 3 over a field acted by an addition operation that forms a group structure. The motivation of this study is the mathematics behind that elliptic curve to the applicability within a ...
E Khamseh
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THEORETICAL ASSUMPTIONS FOR AN INTRODUCTION TO ELLIPTIC CURVE CRYPTOGRAPHY
STED Journal, 2023 Understanding elliptic curves contributed to solving mathematical problems in number theory that had been unsolved for centuries. Elliptic curves were also used in solving one of the millennial problems, which is Fermat's last theorem.
Ognjen Milivojević, Boris Damjanović
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How to Compute an Isogeny on the Extended Jacobi Quartic Curves? [PDF]
International Journal of Electronics and Telecommunications, 2022 Computing isogenies between elliptic curves is a significant part of post-quantum cryptography with many practical applications (for example, in SIDH, SIKE, B-SIDH, or CSIDH algorithms).
Łukasz Dzierzkowski, Michał Wroński
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