Personal tools
You are here: Home / Internal / RISC Forum / 2012 / RISC Colloquium

RISC Colloquium

Prof. Petr Lisonek: Classical modular polynomials over GF(2)
When Sep 24, 2012
from 01:30 PM to 02:30 PM
Where Seminar Room
Add event to calendar vCal
iCal

For a prime number l, the classical modular polynomial Phi_l (sometimes called the modular equation of level l) is a polynomial with integer coefficients such that Phi_l(j(t),j(lt))=0 where j(t) is the j-invariant well known from the theory of elliptic functions.  While it is difficult to compute Phi_l over the integers due to the rapid growth of its coefficients, there is a beautiful structure emerging if one considers Phi_l over GF(2), where it becomes a sparse polynomial.  Even though the modular polynomials considered over GF(2) have important computational applications in elliptic curves cryptography, it appears that the amazing structure of their non-vanishing terms has not been considered in the literature.  By considering the power series expansion of j(q), we prove some necessary conditions that a monomial of Phi_l must satisfy in order to have coefficient 1, and we conjecture many more such conditions based on results from our computational investigations.

« October 2019 »
October
MoTuWeThFrSaSu
123456
78910111213
14151617181920
21222324252627
28293031
Upcoming Events
RISC Forum Oct 28, 2019 01:30 PM - 01:45 PM
RISC Forum Nov 04, 2019 01:30 PM - 01:45 PM
RISC Forum Nov 11, 2019 01:30 PM - 02:30 PM
RISC Forum Nov 18, 2019 01:30 PM - 02:15 PM
RISC Forum Nov 25, 2019 01:30 PM - 01:45 PM
Previous events…
Upcoming events…