New Combinatorial Complete One-Way Functions

Arist Kojevnikov (1) , Sergey I. Nikolenko (1)

1 PDMI RAS - St. Petersburg Department of V.A. Steklov Mathematical Institute

In 2003, Leonid A. Levin presented the idea of a combinatorial complete one-way function and a sketch of the proof that Tiling represents such a function. In this paper, we present two new one-way functions based on semi-Thue string rewriting systems and a version of the Post Correspondence Problem and prove their completeness. Besides, we present an alternative proof of Levin's result. We also discuss the properties a combinatorial problem should have in order to hold a complete one-way function.

Mots clés: cryptography; complete problem; one-way function

Domaines: Complexité [cs.CC]; Cryptographie et sécurité [cs.CR]

Arist Kojevnikov, Sergey I. Nikolenko. New Combinatorial Complete One-Way Functions. STACS 2008, Feb 2008, Bordeaux, France. pp.457-466. ⟨hal-00232966⟩