## 2009 Number Theory Seminar - 08

- Date: 02/26/2009

University of British Columbia

Rational points on curves and cryptography

I'll discuss some connections between algorithms for finding rational

points on curves and some cryptosystems. Akiyama and Goto have proposed

a cryptosystem based on rational points on curves over function fields

(stated in the equivalent form of sections of fibrations on surfaces).

It is easy to construct a curve passing through a few given points, but

finding the points, given only the curve, is hard. In this talk I will

show how to break their original cryptosystem by using algebraic points

instead of rational points and discuss the possibility of changing

their original system to create a secure one.

4:10pm-5:00pm, WMAX 216