Results 71 to 80 of about 811,200 (202)
Efficient arithmetic on subfield elliptic curves over small finite fields of odd characteristic
Journal of Mathematical Cryptology, 2010 In elliptic curve cryptosystems, scalar multiplications performed on the curves have much effect on the efficiency of the schemes, and many efficient methods have been proposed. In particular, recoding methods of the scalars play an important role in the
Hakuta Keisuke +2 more
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On Arithmetic Progressions on Elliptic Curves [PDF]
Experimental Mathematics, 1999 We study arithmetic progressions in the x-coordinates of rational points on elliptic curves. An infinite family of elliptic curves is found, each containing an arithmetic progression of length 8.
openaire +2 more sources
Elliptic Combinatorics and Markov Processes [PDF]
, 2012 We present combinatorial and probabilistic interpretations of recent results in the theory of elliptic special functions (due to, among many others, Frenkel, Turaev, Spiridonov, and Zhedanov in the case of univariate functions, and Rains in the ...
Betea, Dan Dumitru
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Electronic Journal of Differential Equations, 2015 Finite spaces are used on elliptic curves cryptography (ECC) to define the necessary parameters for nonlinear asymmetric cryptography, and to optimize certain solutions of differential equations.
Oana Adriana Ticleanu
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On p-degree of elliptic curves [PDF]
International Journal of Number Theory, 2018 In this note, we investigate the [Formula: see text]-degree function of an elliptic curve [Formula: see text]. The [Formula: see text]-degree measures the least complexity of a non-zero [Formula: see text]-torsion point on [Formula: see text]. We prove some properties of this function and compute it explicitly in some special cases.
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Quadratic Twists of Elliptic Curves [PDF]
, 2011 [[abstract]]Let E be an elliptic curve defined over Q, and for each square-free rational integer d, let E_d denote the the quadratic twist of E by d (in brief, the d-twist). The question concerning the rank rk(Ed(Q)) of the Mordell-Weil group E_d(Q) (the
廖宏銘, Liao, Hung-Min
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Huff’s Model for Elliptic Curves [PDF]
, 2010 This paper revisits a model for elliptic curves over Q introduced by Huff in 1948 to study a diophantine problem. Huff's model readily extends over fields of odd characteristic. Every elliptic curve over such a field and containing a copy of Z/4Z x Z/2Z is birationally equivalent to a Huff curve over the original field.
Marc Joye +2 more
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On Algebraically Integrable Differential Operators on an Elliptic Curve
Symmetry, Integrability and Geometry: Methods and Applications, 2011 We study differential operators on an elliptic curve of order higher than 2 which are algebraically integrable (i.e., finite gap). We discuss classification of such operators of order 3 with one pole, discovering exotic operators on special elliptic ...
Pavel Etingof, Eric Rains
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Parallelizing pairings on Hessian elliptic curves
Arab Journal of Mathematical Sciences, 2019 This paper considers the computation of the Ate pairing on the Hessian model of elliptic curves. Due to the many important properties making the model attractive in cryptography, we compute for the first time the Ate pairing on this model and show how ...
Emmanuel Fouotsa
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Heights on elliptic curves over number fields, period lattices, and complex elliptic logarithms [PDF]
This thesis presents some major improvements in the following computations: a lower bound for the canonical height, period lattices, and elliptic logarithms.
Thongjunthug, Thotsaphon
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