84 search results - page 3 / 17 » Elliptic Curves with a Given Number of Points |
ANTS
2000
Springer
13 years 11 months ago
2000
Springer
Abstract. Essentially all subexponential time algorithms for the discrete logarithm problem over nite elds are based on the index calculus idea. In proposing cryptosystems based on...
EUROCRYPT
2001
Springer
13 years 12 months ago
2001
Springer
The use of elliptic curves in cryptography relies on the ability to count the number of points on a given curve. Before 1999, the SEA algorithm was the only efficient method known ...
IJNSEC
2006
13 years 7 months ago
2006
The joint sparse form (JSF) for the non-adjacent form (NAF) representation of two large integers a and b, was proposed by Solinas. Then Ciet extended it to the -JSF for the -NAF r...
ANTS
2006
Springer
13 years 9 months ago
2006
Springer
Abstract. We give a deterministic polynomial-time algorithm that computes a nontrivial rational point on an elliptic curve over a finite field, given a Weierstrass equation for the...
CHES
2008
Springer
13 years 9 months ago
2008
Springer
Abstract. This paper presents a new shape for ordinary elliptic curves over fields of characteristic 2. Using the new shape, this paper presents the first complete addition formula...