Product Subset Problem : Applications to number theory and cryptography

We consider applications of Subset Product Problem (SPP) in number theory and cryptography. We obtain a probabilistic algorithm that attack SPP and we analyze it with respect time/space complexity and success probability. In fact we provide an application to the problem of finding Carmichael numbers and an attack to Naccache-Stern knapsack cryptosystem, where we update previous results.Comment: 17 pages, 2 figures, LaTeX; references added, typos corrected, a new figure was inserted, sections 2.1, 2.2 improve