I had the opportunity to take several projects in the field of computer security during undergraduate studies at Technion, all of which were in the field of computer security, discussing elliptic curve cryptography.
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.
Recent development in research and practical use of elliptic curves in public key cryptography motivates us to investigate the field: the discrete logarithm problem on elliptic curves is yet to be solved in sub exponential time, we benefit from the same level of security such as one would achieve using RSA whilst using substantially smaller key sizes and digital signatures, noticeably reducing expensive network traffic load in terms of power and transmission time, as well as storage size requirements in favor of computation complexity.
Some of our results are better than some presented in articles.
"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".
On october 2005, Dean Sysman and I won 1st place at the International Robot Oplympiad (IROC) at the creativity category - the most interesting one. There were four stages: theoretical physics exams, robot reconstruction and software tweaking in 4 hours according to the event's theme - assisting the handicapped, presentation and operation, and a design of an unknown concept.
During that year, we developed the cost-efficient robot and designed the software at Technion, under the supervision of Evgeny Korchnoy of the Technion I.I.T.
The robot was built to enable autonomous shaving by using voice commands to control the automated process.