SECANTS
South of England Computational and Algorithmic Number Theory Seminars

11.00-12.00 J. Davenport "Galois Theory and Polynomial Factorization: Effective Links" We investigate how polynomial factorization can make more use of Galois Theory, rather than assume that "polynomials are random".

13.30-14.00 P. Leyland "A Hostile Attack on an RSA Key" A group of 4 people with modest resources factored a 384-bit RSA key with PPMPQS over 3 months --- entirely unnoticed. 512-bit keys are now vulnerable to hostile attack, putting gigabucks at risk.

14.00-15.00 R. Pinch "Back to the Dark Ages: a new look at some old factoring methods"
In recent years, there has been spectacular progress in the practical art of factoring. By contrast, the theoretical problem of finding deterministic algorithms which provably factor composite numbers has made little, if any, progress. In this talk, I report on joint work with James McKee examining some old exponential-time ("Dark Ages") deterministic algorithms: we give deterministic running times for them, and provide several new examples of algorithms of this type.

15.15-16.15 S. Siksek "Infinite Descent on Elliptic Curves"