What level of crypto security?

The security level for Elliptic Curve Cryptography is determined by the cardinality of the group rational points. The group order has to be known to generate secure elliptic curves. In other words: we need to pick a curve of known order.

Two main approaches to do this are:

1. Random approach

a. Pick random paramaters a and b

b. Use point counting algorithm for finding the group order

2. Complex multiplication approach

a. Define the group order candidates

b. Determine a and b using complex multiplication

I’m still digesting this dissertation about algorithm for determining cardinality to limit the complexity (whatever that means 😉 )

Will add more details on this, very soon!

[Sources: Harald Baier dissertation and Intan’s notes]