ANTS
2004
Springer
14 years 5 months ago
2004
Springer
In this paper we investigate the efficiency of the function field sieve to compute discrete logarithms in the finite fields F3n . Motivated by attacks on identity based encrypti...
ANTS
2004
Springer
14 years 5 months ago
2004
Springer
In this paper, we study p-divisibility of discriminants of Hecke algebras associated to spaces of cusp forms of prime level. By considering cusp forms of weight bigger than 2, we a...
ANTS
2004
Springer
14 years 5 months ago
2004
Springer
We discuss the situation where a curve C, defined over a number field K, has a known K-rational divisor class of degree 1, and consider whether this class contains an actual K-ra...
ANTS
2004
Springer
14 years 5 months ago
2004
Springer
We present a non-archimedean method to construct, given an integer N ≥ 1, a finite field Fq and an elliptic curve E/Fq such that E(Fq) has order N.
ANTS
2004
Springer
14 years 5 months ago
2004
Springer
Using powerful tools on genus 2 curves like the Kummer variety, we generalize the Montgomery method for scalar multiplication to the jacobian of these curves. Previously this metho...
ANTS
2004
Springer
14 years 5 months ago
2004
Springer
Given an algebraic number field K, such that [K : Q] is constant, we show that the problem of computing the units group O∗ K is in the complexity class SPP. As a consequence, w...
ANTS
2004
Springer
14 years 5 months ago
2004
Springer
On the lines of the binary gcd algorithm for rational integers, algorithms for computing the gcd are presented for the ring of integers in Q( √ d) where d ∈ {−2, −7, −11,...
ANTS
2004
Springer
14 years 5 months ago
2004
Springer
We present algorithms for computing the squared Weil and Tate pairings on an elliptic curve and the squared Tate pairing for hyperelliptic curves. The squared pairings introduced i...