Advances in Cryptology

The undecidable word problem for groups and semlgroups is investigated as a basis for a public-key cryptosystem. A specific approach is discussed along with the results of an experimental implementation. This approach does not give a provably secure or practical system, but shows the type of cryptosystem that could be constructed around the word problem. This cryptosystem is randomized, with infinitely many ciphertexts corresponding t o each plaintext. 1. NP-COMPLETE PROBLEMS. The idea of using an NP-complete problem to construct a public-key cryptosystem (PKC) seemed promising [Diff76], but has not been successful historically. The earliest such PKC was based on the integer knapsack problem, and recently various versions of this PKC have been broken by general, powerful attacks [Sha83al, IAdle831. (In this case, the attacks have been carried out on the type of trapdoor inserted, and not directly on the This work was supported in part by NSF grant DCR-8403350, and by Drexel University's Faculty Development Mini-Grant program G.R. Blakley and D. Chaum (Eds.): Advances in Cryptology CRYPT0 '84, LNCS 196, pp. 19-36, 1985. 0 Springer-Verlag Berlin Heidelberg 1985

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