| dc.contributor.advisor | Veni Madhavan, C E | |
| dc.contributor.author | Ramesh, Athale Rahul | |
| dc.date.accessioned | 2025-10-15T11:24:47Z | |
| dc.date.available | 2025-10-15T11:24:47Z | |
| dc.date.submitted | 1999 | |
| dc.identifier.uri | https://etd.iisc.ac.in/handle/2005/7204 | |
| dc.description.abstract | Hasse’s theorem states that:ifE {W g) Then |i| < 2y/q.
This gives the bound on the number of points. In 1985, Schoof presented a polynomial time
algorithm for computing The algorithm has running time of 0(log® q) bit operations.
We discuss our efficient implementation of this algorithm over lF2m fields using the g F L
Library, developed by Abhijit Das and C.E. Veni Madhavan. The implementation requires
the computation of polynomial exponentiation and product modulo another polynomial of the
order of 0(log^ q) . The degrees of the polynomials involved are very large. We have made the
implementation efficient by optimizing the intermediate computations.
We also study the structure of the group of points on the elliptic curves, for the fields up
to F211 - We have written different routines for the elliptic curve point addition, multiplication
etc. for this study. We have also implemented an ElGamal cryptosystem using the elliptic curve
group over F2m fields | |
| dc.language.iso | en_US | |
| dc.relation.ispartofseries | T04594 | |
| dc.rights | I grant Indian Institute of Science the right to archive and to make available my thesis or dissertation in whole or in part in all forms of media, now hereafter known. I retain all proprietary rights, such as patent rights. I also retain the right to use in future works (such as articles or books) all or part of this thesis or dissertation | |
| dc.subject | Elliptic Curve Cryptography | |
| dc.subject | ElGamal Cryptosystem | |
| dc.subject | Parallel Computing | |
| dc.title | Counting number of points on elliptic curves over F2m fields : An implementation study | |
| dc.type | Thesis | |
| dc.degree.name | MSc Engg | |
| dc.degree.level | Masters | |
| dc.degree.grantor | Indian Institute of Science | |
| dc.degree.discipline | Engineering | |
