# SECANTS

South of England Computational and Algorithmic Number Theory Seminars

##
First Meeting

Saturday 2 December 1995

Oxford (Mathematical Institute)

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"**

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