Point counting on elliptic curves
Event details
| Date | 07.11.2016 |
| Hour | 10:00 › 12:00 |
| Speaker | Dusan Kostic |
| Location | |
| Category | Conferences - Seminars |
EDIC Candidacy Exam
Exam President: Prof. Ola Svensson
Thesis Director: Prof. Arjen Lenstra
Co-examiner: Prof. Dimitar Jetchev
Background papers
Counting points on elliptic curves over finite fields, (1995), by R. Schoof.
Computing modular polynomials, (2004), by D. Charles, K. Lauter.
Efficient ephemeral elliptic curve cryptographic keys, (2015), by A. Miele, A.K. Lenstra.
Abstract
Generating secure elliptic curves is an essential part in elliptic curve cryptographic systems. Number of points on the curve plays an important role in the assessment of the curve security. This write-up investigates the most efficient algorithm for general point counting - Schoof-Elkies-Atkin algorithm, a method for constructing modular polynomials, and a complex multiplication based method for generating elliptic curves. Re- search directions in the area of curve generation are then discussed.
Exam President: Prof. Ola Svensson
Thesis Director: Prof. Arjen Lenstra
Co-examiner: Prof. Dimitar Jetchev
Background papers
Counting points on elliptic curves over finite fields, (1995), by R. Schoof.
Computing modular polynomials, (2004), by D. Charles, K. Lauter.
Efficient ephemeral elliptic curve cryptographic keys, (2015), by A. Miele, A.K. Lenstra.
Abstract
Generating secure elliptic curves is an essential part in elliptic curve cryptographic systems. Number of points on the curve plays an important role in the assessment of the curve security. This write-up investigates the most efficient algorithm for general point counting - Schoof-Elkies-Atkin algorithm, a method for constructing modular polynomials, and a complex multiplication based method for generating elliptic curves. Re- search directions in the area of curve generation are then discussed.
Practical information
- General public
- Free
Contact
- Cecilia Chapuis EDIC