[ Changed 5th June 1998 ]
The talk will be based loosely around the use of partial knowledge in solving bivariate Diophantine equations. Many interesting problems fall in to this category including factoring, and solving univariate modular equations, both of which have major implications in cryptography.
The methods are based on work by Coppersmith, and employ lattice basis reduction by the LLL algorithm. An interesting theoretical result concerning dual lattices and the LLL algorithm is shown along the way.
Finally a novel approach to fiding solutions to x^2+y^2=N is demonstrated, and applied (using the technique of Pinch and McKee) to breaking a recently proposed elliptic curve cryptosystem.