Ph.D. started in: 2016
Expected year of graduation: 2019
COINS consortium member: University of Bergen
Supervised by: Igor A. Semaev, Tor Helleseth
Research area: Cryptography
Project title: Analysis of Macaulay matrices over finite fields
Project description: Elliptic curve cryptography algorithms have been of common use for a decade. Unlike DLPs in finite field, there are no dedicated algorithms for solving the discrete logarithm over the groupof points on an elliptic curve significantly faster than Pollard’s rho. Semaev proposed an elliptic curve version for index calculus algorithms. Experimental results show that the algorithm is actually faster than Pollard’s rho. Our goal is to prove formally that the average complexity is smaller than known methods. In order to do this, we require a deep understanding of the Macaulay matrices that lead to the generation of the Gröbner basis that finds solutions for the summation polynomials used to write a point on the curve as sum of points whose logarithms are known.
- COINS Finse winter school, Finse, Norway, 2017