Results 41 to 50 of about 136,439 (162)
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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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.
José Felipe Voloch +2 more
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A NEW PROPOSED METHOD FOR SOLVING AN ELLIPTIC CURVE DISCRETE LOGARITHM PROBLEM
Journal of Kufa for Mathematics and Computer, 2012 In this work, we present a new approach for solving Elliptic Curve Discrete Logarithm Problem. This method provides a new access to the field of attacking methods the Elliptic Curve Cryptosystems.
Ammar Ali Neamah
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ED25519: A New Secure Compatible Elliptic Curve for Mobile Wireless Network Security
Jordanian Journal of Computers and Information Technology, 2022 Wireless Sensor Networks (WSNs) create various security threats such as application variance in different sectors along with the model of cryptographic primitive and necessity.
MAUSAM DAS, Zenghui Wang
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Lam\'e polynomials, hyperelliptic reductions and Lam\'e band structure
, 2004 The band structure of the Lam\'e equation, viewed as a one-dimensional Schr\"odinger equation with a periodic potential, is studied. At integer values of the degree parameter l, the dispersion relation is reduced to the l=1 dispersion relation, and a ...
Arscott F.M +11 more
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Aperiodic Photonics of Elliptic Curves [PDF]
Crystals, 2019 In this paper we propose a novel approach to aperiodic order in optical science and technology that leverages the intrinsic structural complexity of certain non-polynomial (hard) problems in number theory and cryptography for the engineering of optical media with novel transport and wave localization properties.
Negro, Luca Dal Dal +2 more
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Elliptic Curves - an Introduction [PDF]
Irish Mathematical Society Bulletin, 2007 Elliptic curves – an introduction ...
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Auxetic deformations and elliptic curves [PDF]
Computer Aided Geometric Design, 2018 The problem of detecting auxetic behavior, originating in materials science and mathematical crystallography, refers to the property of a flexible periodic bar-and-joint framework to widen, rather than shrink, when stretched in some direction. The only known algorithmic solution for detecting infinitesimal auxeticity is based on the rather heavy ...
Ciprian S. Borcea, Ileana Streinu
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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
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Bilinear pairings on elliptic curves [PDF]
L’Enseignement Mathématique, 2016 We give an elementary and self-contained introduction to pairings on elliptic curves over finite fields. The three different definitions of the Weil pairing that can be found in the literature are stated and proved to be equivalent using Weil reciprocity. Pairings with shorter loops, such as the ate, ate _i
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