Abstract

The first part of this paper gives results about promise problems. A "promise problem " is a formulation of a partial decision problem that is useful for describing cracking problems for publickey cryptosystems (PKCS). We prove that every NPhard promise problem is uniformly NP-hard, and we show that a number of results and a conjecture about promise problems are equivalent to separability assertions that are the natural analogues of well-known results in classical recursion theory. The conjecture, if it is true, implies nonexistence of PKCS having NP-hard cracking problems. The second part of the paper studies more appropriate measures for PKCS. Among the results obtained are the following: One-way functions exist if and only if P # and one-way functions f such that range f E P exist if and only if U n CO-U # P. It will follow that there exist PKCS that cannot be cracked in polynomial time (and that satisfy other reasonable assumptions) only if P # U. 1.

Citations