Creating strong, total, commutative, associative one-way functions from any one-way function in complexity theory

Abstract

Rabi and Sherman presented novel digital signature and unauthenticated secret-key agreement protocols, developed by themselves and by Rivest and Sherman. These protocols use strong, total, commutative (in the case of multiparty secret-key agreement), associative one-way functions as their key building blocks. Although Rabi and Sherman did prove that associative one-way functions exist if P ≠ NP, they left as an open question whether any natural complexity-theoretic assumption is sufficient to ensure the existence of strong, total, commutative, associative one-way functions. In this paper, we prove that if P ≠ NP then strong, total, commutative, associative one-way functions exist.