In a two-party communication where one party knows a secret, how can he convince the other without sharing any information regarding the secret?
Here we address the question, "how does a weak verifier (or several weak and isolated verifiers) interrogates powerful but isolated provers in order to ascertain something outside of its computational powers
This is a multidisciplinary area where we investigate the cryptographic, number theroretic and implementation aspects of elliptic curves. Elliptic curves are currently used for an implementation of factoring problem where they render a fast key exchange, particularly in embedded devices such as cell-phones. In the post-quantum world where the hardness assumption of the factoring problem is no longer valid we look at the other presumably hard problems, in particular Supersingular Isogeny Diffe-Hellman defined on elliptic curves.
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