Results 1 to 10 of about 2,536,804 (344)
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
semanticscholar +3 more sources
A classification of isogeny‐torsion graphs of Q‐isogeny classes of elliptic curves
Transactions of the London Mathematical Society, 2021 Let E be a Q‐isogeny class of elliptic curves defined over Q. The isogeny graph associated to E is a graph which has a vertex for each elliptic curve in the Q‐isogeny class E, and an edge for each cyclic Q‐isogeny of prime degree between elliptic curves ...
Garen Chiloyan, Álvaro Lozano‐Robledo
doaj +2 more sources
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
doaj +2 more sources
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
doaj +2 more sources
An exploration of affine group laws for elliptic curves
Journal of Mathematical Cryptology, 2011 Several forms of elliptic curves are suggested for an efficient implementation of Elliptic Curve Cryptography. However, a complete description of the group law has not appeared in the literature for most popular forms.
Hisil Huseyin +3 more
doaj +2 more sources
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
Computation of Trusted Short Weierstrass Elliptic Curves for Cryptography
Cybernetics and Information Technologies, 2021 Short Weierstrass elliptic curves with underlying hard Elliptic Curve Discrete Logarithm Problem (ECDLP) are widely used in cryptographic applications. A notion of security called Elliptic Curve Cryptography (ECC) security is also suggested in literature
Abhishek Kunal +1 more
doaj +1 more source