THE COMPLEXITY OF PROMISE PROBLEMS WITH APPLICATIONS TO PUBLIC-KEY CRYPTOGRAPHY

A 'promise problem' is a formulation of a partial decision problem. Complexity issues about promise problems arise from considerations about cracking problems for public-key cryptosystems. Using a notion of Turing reducibility between promise problems, this paper disproves a conjecture that would imply nonexistence of public-key cryptosystems with NP-hard cracking problems. In its place a new conjecture is raised having the same consequence. In addition, the new conjecture implies that NP-complete sets cannot be accepted by Turing machines that have at most one accepting computation for each input word.