We present a computational method for solving a single quadratic equation in two unknowns which are constrained to be integers from bounded intervals. We give heuristic estimates of the running time in terms of the parameters. We then apply this method to the problem of finding the factors P,Q of an integer N=PQ when given many high order bits of P and Q. If each of P,Q has m bits and we know the high order ((0.6m)-L) bits of P, we heuristically expect to find the factorization after a computation of length O(2**L). We also treat the case where we know the high order bits of a multiple of Q.
By: Don Coppersmith
Published in: RC20089 in 1995
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