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

Rabi and Sherman presented novel digital signature and unauthenticated secr et-key agreement protocols, developed by themselves and by Rivest and Sherm an. These protocols use strong, total, commutative (in the case of multipar ty secret-key agreement), associative one-way functions as their key buildi ng blocks. Although Rabi and Sherman did prove that associative one-way fun ctions exist if P not equal NP, they left as an open question whether any n atural complexity-theoretic assumption is sufficient to ensure the existenc e of strong, total, commutative, associative one-way functions. Tn this pap er, we prove that if P not equal NP then strong, total, commutative, associ ative one-way functions exist. (C) 1999 Academic Press.