Global duality, signature calculus and the discrete logarithm problem

Details Global duality, signature calculus and the discrete logarithm problem Global duality, signature calculus and the discrete logarithm problem

2007-10-11

arxiv.org/abs/0710.2363v1

Mathematics

Number Theory

Scientific paper

We study the discrete logarithm problem for the multiplicative group and for elliptic curves over a finite field by using a lifting of the corresponding object to an algebraic number field and global duality. We introduce the \textit{signature} of a Dirichlet character (in the multiplicative group case) or principal homogeneous space (in the elliptic curve case), which is a measure of the ramification at certain places. We then develop \textit{signature calculus}, which generalizes and refines the index calculus method. Finally, we show the random polynomial time equivalence for these two cases between the problem of computing signatures and the discrete logarithm problem.

Affiliated with

Also associated with

No associations

Rating

Global duality, signature calculus and the discrete logarithm problem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Global duality, signature calculus and the discrete logarithm problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Global duality, signature calculus and the discrete logarithm problem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-402585