Results 61 to 70 of about 811,200 (202)

Multiplication polynomials and relative Manin-Mumford [PDF]

, 2015
After the introduction we prove in chapter 2 that the resultant of the standard multiplication polynomials $A_n,B_n$ of an elliptic curve in the form $y^2 = x^3+ax+b$ is
$(16\Delta)^{{n^2(n^2-1) \over 6}}$, where $\Delta=-(4a^3+27b^2)$ is the ...
Schmidt, Harry
core   +1 more source

Iwasawa theory for modular forms at supersingular primes [PDF]

, 2010
Let f=\sum a_nq^n be a normalised eigen-newform of weight k\ge2 and p an odd prime which does not divide the level of f. We study a reformulation of Kato's main conjecture for f over the Zp-cyclotomic extension of Q.
Antonio Lei
core   +2 more sources

Lattices and Rational Points

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

On the Search for Supersingular Elliptic Curves and Their Applications

Mathematics
Elliptic curves with the special quality known as supersingularity have gained much popularity in the rapidly developing field of cryptography. The conventional method of employing random search is quite ineffective in finding these curves.
Ismel Martinez-Diaz, Rashad Ali, Muhammad Kamran Jamil   +2 more
doaj   +1 more source

Application of mathematical optimization in elliptic curve arithmetic

Безопасность информационных технологий, 2017
Currently, a lot of standardized elliptic curve cryptographic algorithms are widely used. Due to the constantly increasing execution speed demands, implementation optimization problem become actual.
Alexander Igorevich Skripko, Alexander Nikolaevich Veligura   +1 more
doaj   +1 more source

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.
Pierre-Alain Fouque, Antoine Joux, Mehdi Tibouchi   +2 more
openaire   +3 more sources

Average Analytic Ranks of Elliptic Curves over Number Fields

Forum of Mathematics, Sigma
We give a conditional bound for the average analytic rank of elliptic curves over an arbitrary number field. In particular, under the assumptions that all elliptic curves over a number field K are modular and have L-functions which satisfy the ...
Tristan Phillips
doaj   +1 more source

Torsion groups of a family of elliptic curves over number fields [PDF]

, 2006
summary:We compute the torsion group explicitly over quadratic fields and number fields of degree coprime to 6 for a family of elliptic curves of the form $E\colon y^2 = x^3 +c$, where $c$ is an ...
Dey, Pallab Kanti, Raymond Ayoub
core   +1 more source

Faster Complete Addition Laws for Montgomery Curves

Transactions on Cryptographic Hardware and Embedded Systems
An addition law for an elliptic curve is complete if it is defined for all possible pairs of input points on the elliptic curve. In Elliptic Curve Cryptography (ECC), a complete addition law provides a natural protection against side-channel attacks ...
Reza Rezaeian Farashahi, Mojtaba Fadavi, Soheila Sabbaghian   +2 more
doaj   +1 more source

Heuristics on pairing-friendly elliptic curves

Journal of Mathematical Cryptology, 2012
We present a heuristic asymptotic formula as for the number of isogeny classes of pairing-friendly elliptic curves over prime fields with fixed embedding degree , with fixed discriminant, with rho-value bounded by a fixed such that , and with prime ...
Boxall John
doaj   +1 more source