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.
@InProceedings{kojevnikov_et_al:LIPIcs.STACS.2008.1365, author = {Kojevnikov, Arist and Nikolenko, Sergey I.}, title = {{New Combinatorial Complete One-Way Functions}}, booktitle = {25th International Symposium on Theoretical Aspects of Computer Science}, pages = {457--466}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-06-4}, ISSN = {1868-8969}, year = {2008}, volume = {1}, editor = {Albers, Susanne and Weil, Pascal}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1365}, URN = {urn:nbn:de:0030-drops-13652}, doi = {10.4230/LIPIcs.STACS.2008.1365}, annote = {Keywords: } }
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