A general polynomial sieve

An important component of the index calculus methods for finding discrete l ogarithms is the acquisition of smooth polynomial relations. Gordon and McC urley (1992) developed a sieve to aid in finding smooth Coppersmith polynom ials for use in the index calculus method. We discuss their approach and so me of the difficulties they found with their sieve. We present a new sievin g method that can be applied to any affine subspace of polynomials over a f inite field.