Results 1 to 10 of about 699,908 (302)
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
Journal of Mathematical Cryptology, 2018 In 2004, Muzereau, Smart and Vercauteren [A. Muzereau, N. P. Smart and F. Vercauteren, The equivalence between the DHP and DLP for elliptic curves used in practical applications, LMS J. Comput. Math. 7 2004, 50–72] showed how to use a reduction algorithm
Kushwaha Prabhat
doaj +1 more source
Journal of Number Theory, 1993 Let \(J_ 0(N)/ \mathbb{Q}\) denote the Jacobian of the modular curve \(X_ 0(N)/ \mathbb{Q}\). Fix a prime \(p \geq 5\), and let \(K\) denote the maximal unramified extension of \(\mathbb{Q}_ p\). Given an abelian variety \(A/K\), the connected component of zero of the special fiber of its Néron model is an extension of an abelian variety of dimension \(
openaire +2 more sources
Aperiodic Photonics of Elliptic Curves
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 ...
Luca Dal Negro +2 more
doaj +1 more source
Boundary asymptotics of the relative Bergman kernel metric for hyperelliptic curves
Complex Manifolds, 2017 We survey variations of the Bergman kernel and their asymptotic behaviors at degeneration. For a Legendre family of elliptic curves, the curvature form of the relative Bergman kernel metric is equal to the Poincaré metric on ℂ \ {0,1}. The cases of other
Dong Robert Xin
doaj +1 more source
Homogeneous Mapping Model of ECC for Preventing Differential Power Analysis [PDF]
Jisuanji gongcheng, 2017 Existing public key research is based on increasing the redundance operation of Elliptic Curve Cryptosystems(ECC) aginst Differential Power Analysis(DPA) attacks,it causes ECC efficiency low,and affects the application of ECC in computation resource ...
WU Keke,LI Huiyun,YAN Lijun
doaj +1 more source
Euler characteristics and elliptic curves [PDF]
Proceedings of the National Academy of Sciences, 1997 Let E be a modular elliptic curve over ℚ, without complex multiplication; let p be a prime number where E has good ordinary reduction; and let F ∞ be ...
Coates, John, Howson, Susan
openaire +3 more sources
Injective Encodings to Elliptic Curves [PDF]
, 2013 For a number of elliptic curve-based cryptographic protocols, it is useful and sometimes necessary to be able to encode a message (a bit string) as a point on an elliptic curve in such a way that the message can be efficiently and uniquely recovered from the point.
Fouque, Pierre-Alain +2 more
openaire +3 more sources
Mathematics, 2017 In this article, we show how to use the first and second Minkowski Theorems and some Diophantine geometry to bound explicitly the height of the points of rank N - 1 on transverse curves in E N , where E is an elliptic curve without Complex
Evelina Viada
doaj +1 more source
Elliptic nets and elliptic curves [PDF]
Algebra & Number Theory, 2011 An elliptic divisibility sequence is an integer recurrence sequence associated to an elliptic curve over the rationals together with a rational point on that curve. In this paper we present a higher-dimensional analogue over arbitrary base fields. Suppose E is an elliptic curve over a field K, and P_1, ..., P_n are points on E defined over K.
openaire +3 more sources