International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Annegret Weng

Publications

Year
Venue
Title
2004
EPRINT
Generation of random Picard curves for cryptography
Annegret Weng
Based on ideas in an earlier paper by Mark Bauer, Edlyn Teske and myself and ideas of Pierrick Gaudry and Eric Schost, we present an algorithm for counting the number of elements in the Jacobian of a random Picard curve over a finite prime field of cryptosize. We give two examples of curves with a Jacobian of prime group order.
2003
EPRINT
Weak Fields for ECC
Alfred Menezes Edlyn Teske Annegret Weng
We demonstrate that some finite fields, including GF(2^210) are weak for elliptic curve cryptography in the sense that any instance of the elliptic curve discrete logarithm problem for any elliptic curve over these fields can be solved in significantly less time than it takes Pollard's rho method to solve the hardest instances. We discuss the implications of our observations to elliptic curve cryptography, and list some open problems.
2003
EPRINT
Elliptic curves suitable for pairing based cryptography
Friederike Brezing Annegret Weng
We give a method for constructing ordinary elliptic curves over finite prime field $\mathbb{F}_p$ with small security parameter $k$ with respect to a prime $\ell$ dividing the group order $\#E(\mathbb{F}_p)$ such that $p<<\ell^2$.