ECC is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields.

We chose to focus on a memory efficient algorithm variant of Satoh's algorithm, extending it to characteristic two, for counting the number of points on a given curve in order to to check whether it is divisible by a large prime number q, find a point p s.t. ord(p) is q, and then use the cyclic subgroup defined by <p>, the generating group of p, which is cryptographically strong due to the algebraic properties its elements acquire.

Pairing-based public key cryptography; in the words of the our mentor, Barukh Ziv:

"This is a fascinating new topic, which allows building unique PK systems, like Identity-Based Encryption. View pairing as a special map from 2 points on Elliptic Curve to multiplicative group of integers modulo big prime. Pairings were originally used for attacks on 'weak' Elliptic Curves. In 2000-s,constructive development of Cryptographic Schemes previously unknown or impractical: Short Digital Signatures, 1-Pass Three Person Key Exchange, Identity-Based Encryption. 'Communicating one bit of data uses significantly more power than executing one 32-bit instruction', Barr and Asanovich 2003".

Technical assistance had been provided.