In this paper we consider the difficulty of factoring multivariate polynomials F(z, y, z,...) modulo n. We consider in particular the case in which F is a product of two randomly chosen polynomials P and Q with algebraically specified coefficients, and n is the product of two randomly chosen primes p and q. The general problem of factoring 1’ is known to be at least as hard as the factorization of n, but in many restricted cases (when P or Q are known to have a particular form) the problem can be much easier. The main result of this paper is that (with one trivial exception), the problem of factoring F is at least as hard as the factorization of n whenever P and Q are randomly chosen from the same sample space, regardless of what may be known
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