# Finding a Small Root of a Bivariate Integer Equation; Factoring with High Bits Known

We present a method to solve integer polynomial equations in two variables, provided that the solution is suitably bounded. As an application, we show how to find the factors of $N=PQ$ if we are given the high order $(1/4 + \epsilon) (log N)$ bits of $P$. This compares with Rivest and Shamir's factor 1/3.

By: Don Coppersmith

Published in: RC20280 in 1995

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