35 search results - page 5 / 7 » On the Construction of Prime Order Elliptic Curves |
MOC
2010
13 years 1 months ago
2010
We give an elementary way to distinguish between the twists of an ordinary elliptic curve E over Fp in order to identify the one with p+1-2U points, when p = U2 + dV 2 with 2U, 2V ...
EUROCRYPT
1999
Springer
13 years 10 months ago
1999
Springer
In this paper we discuss various aspects of cryptosystems based on hyperelliptic curves. In particular we cover the implementation of the group law on such curves and how to genera...
PAIRING
2010
Springer
13 years 4 months ago
2010
Springer
This paper describes the design of a fast software library for the computation of the optimal ate pairing on a Barreto–Naehrig elliptic curve. Our library is able to compute the ...
TIT
2010
13 years 29 days ago
2010
In this paper we introduce the concept of an optimal pairing, which by definition can be computed using only log2 r/(k) basic Miller iterations, with r the order of the groups invo...
ANTS
2010
Springer
13 years 10 months ago
2010
Springer
Abstract. Mazur proved that any element ξ of order three in the Shafarevich-Tate group of an elliptic curve E over a number field k can be made visible in an abelian surface A in...