منابع مشابه
Deformations and Hecke Curves
Following Andrew Wiles' announcement of his work, in June 1993, and in view of the immense interest it met with, I felt it reasonable to give a two semester graduate course 1 covering topics that might be helpful to people who want to understand, and possibly pursue, the ~. / subject. In the Fall semester I covered the basic deformation theory of Galois representations (in detail) and Fontaine'...
متن کاملElliptic Nets and Elliptic Curves
Elliptic divisibility sequences are integer recurrence sequences, each of which is 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 P1, . . . , Pn are points on E defined over K. To this information we associate an ...
متن کاملGeneralized Jacobian and Discrete Logarithm Problem on Elliptic Curves
Let E be an elliptic curve over the finite field F_{q}, P a point in E(F_{q}) of order n, and Q a point in the group generated by P. The discrete logarithm problem on E is to find the number k such that Q = kP. In this paper we reduce the discrete logarithm problem on E[n] to the discrete logarithm on the group F*_{q} , the multiplicative group of nonzero elements of Fq, in the case where n | q...
متن کاملElliptic Curves and Cryptography
results in more than 30.000 hits, ranging from articles in mathematics and computer science to books and implementations and applications of the algorithms. There are a lot of different algorithms and also different ways to attack them, many of them involving a huge amount of theory. Moreover, the fact that still there is not an accepted standard on elliptic curve cryptography benefits the exis...
متن کاملElliptic Curves and Cryptography
Elliptic curves also figured prominently in the recent proof of Fermat's Last Theorem by Andrew Wiles. Originally pursued for purely aesthetic reasons, elliptic curves have recently been utilized in devising algorithms for factoring integers, primality proving, and in public-key cryptography. In this article, we aim to give the reader an introduction to elliptic curve cryptosystems, and to demo...
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ژورنال
عنوان ژورنال: Computer Aided Geometric Design
سال: 2018
ISSN: 0167-8396
DOI: 10.1016/j.cagd.2018.02.003