Showing papers on "Weil pairing published in 1993"
Journal Article•
TL;DR: For every pair of positive integers m and n with m dividing the GCD of n and q-1, the authors construct a modular curve over F_q that parametrizes elliptic curves along with F-q-defined points P and Q with P and (n/m)Q having a given Weil pairing.
Abstract: Given a prime power q, for every pair of positive integers m and n with m dividing the GCD of n and q-1, we construct a modular curve over F_q that parametrizes elliptic curves over F_q along with F_q-defined points P and Q of order m and n, respectively, with P and (n/m)Q having a given Weil pairing. Using these curves, we estimate the number of elliptic curves over F_q that have a given integer N dividing the number of their F_q-defined points.
41 citations
Journal Article•
TL;DR: In this paper, Menezes, Okamoto and Vanstone proposed a method that reduces EDLP to DLP, which gave an impact on the security of cryptosystems based on EDLP.
Abstract: In 1990, Menezes, Okamoto and Vanstone proposed a method that reduces EDLP to DLP, which gave an impact on the security of cryptosystems based on EDLP. But this reducing is valid only when Weil pairing can be defined over the m-torsion group which includes the base point of EDLP. If an elliptic curve is ordinary, there exists EDLP to which we cannot apply the reducing. In this paper, we investigate the condition for which this reducing is invalid. key words: Public-key, Discrete logarithms, Elliptic curves.
4 citations