Results 51 to 60 of about 94 (71)
Isogenies for point counting on genus two hyperelliptic curves with maximal real multiplication
, 2017 Schoof's classic algorithm allows point-counting for elliptic curves over finite fields in polynomial time. This algorithm was subsequently improved by Atkin, using factorizations of modular polynomials, and by Elkies, using a theory of explicit ...
Ballentine, Sean +9 more
core +2 more sources
Théorie des nombres et cryptographie
, 2014 Modern cryptographic constructions are based on constructions from number theory, but many of the links go deeper than typically realized. The development of modern cryptography runs in parallel to developments and central questions in number theory ...
Kohel, David, Shparlinski, Igor E.
core +1 more source
UEG Week 2024 Poster Presentations
United European Gastroenterology Journal, Volume 12, Issue S8, Page 665-1360, October 2024.
wiley +1 more source
New methods for finite field arithmetic [PDF]
We describe novel methods for obtaining fast software implementations of the arithmetic operations in the finite field GF(p) and GF(p[superscript k]). In GF(p) we realize an extensive speedup in modular addition and subtraction routines and some small ...
Yanik, Tuğrul
core +1 more source
Elliptic Gau{\ss} sums and Schoof's algorithm
, 2016 We present a new approach to handling the case of Atkin primes in Schoof's algorithm for counting points on elliptic curves over finite fields. Our approach is based on the theory of polynomially cyclic algebras, which we recall as far as necessary. We then proceed to describe our method, which essentially relies on transferring costly computations in ...
openaire +1 more source
Counting the points on elliptic curves over finite fields
, 2018 The goal of this thesis is to explain and implement Schoof's algorithm for counting points on elliptic curves over finite fields. We start by defining elliptic curve as a set of points satisfying certain equation and then proceeding to define an ...
Eržiak, Igor
core
Elliptic Curve Cryptography and Point Counting Algorithms [PDF]
, 2012 Hailiza Kamarulhaili, Liew Khang Jie
core +1 more source
, 2006 Elliptic curves have a rich mathematical history dating back to Diophantus (c. 250 C.E.), who used a form of these cubic equations to find right triangles of integer area with rational sides. In more recent times the deep mathematics of elliptic curves
McGee, John J.
core
The order elliptic curves over finite fields of characteristic two using the Schoof algorithm
The order elliptic curves over finite fields of characteristic two using the Schoof algorithmThe elliptic curve cryptosystem is a popular cryptosystem. Its safety depends on the difficulty of the elliptic curve discrete logarithm problem (ECDLP). From the viewpoint of ECDLP, it is very interesting to determine the order of elliptic curves.
openaire