On the generation of multivariate polynomials which are hard to factor

In this paper we consider the di culty of factoring multivariate polynomials F(x 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 speci ed coe cients, and n is the product of two randomly chosen primes p and q. The general problem of factoring F 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 about its form.

• Type: Conference
• Year: 1993
• Where: STOC
• Authors: Adi Shamir
• Keywords: Algorithms, Multivariate Polynomials, Randomly, Speci Ed Coe, STOC 1993