My research and investigations

Elliptic Curve 2

The theory of elliptic curves (EC) can go very deep, but its applications (see here) need only an understanding of the group law which is unique to elliptic curves. Many algorithms of these applications work for any group, although the special structure of the elliptic curve group has implications in reliability (e.g. cryptography) or efficiency (e.g. factoring) of the algorithm.

Originally, my plan for the project work on this topic is to do the following:

  1. Formalize elementary group theory from its axioms
  2. Extend this formalization to include the group structure of elliptic curves

Then use this formalization to verify EC algorithms. However:

Since Romain Cosse haven’t published formal proofs of his new EC factorization algorithms, I may be able to fill in this gap by building upon the works of Joe and Laurent.

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: