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Groups Complexity Cryptology

Managing Editor: Rosenberger, Gerhard / Shpilrain, Vladimir

Editorial Board Member: Blackburn, Simon R. / Conder, Marston / Dehornoy, Patrick / Eick, Bettina / Fine, Benjamin / Gilman, Robert / Grigoriev, Dima / Ko, Ki Hyoung / Kreuzer, Martin / Mikhalev, Alexander V. / Myasnikov, Alexei / Roman'kov, Vitalii / Sapir, Mark / Schäge, Sven / Thomas, Rick / Tsaban, Boaz / Capell, Enric Ventura / Weil, Pascal

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Generic Case Complexity and One-Way Functions

Alex D. Myasnikov1

1Department of Mathematical Sciences, Stevens Institute of Technology, Hoboken, NJ 07030, USA.

Citation Information: Groups – Complexity – Cryptology. Volume 1, Issue 1, Pages 13–31, ISSN (Online) 1869-6104, ISSN (Print) 1867-1144, DOI: 10.1515/GCC.2009.13, February 2010

Publication History

Received:
2008-01-07
Published Online:
2010-02-18

The goal of this paper is to introduce ideas and methodology of the generic case complexity to cryptography community. This relatively new approach allows one to analyze the behavior of an algorithm on “most” inputs in a simple and intuitive fashion which has some practical advantages over classical methods based on averaging.

We present an alternative definition of one-way function using the concepts of generic case complexity and show its equivalence to the standard definition. In addition we demonstrate the convenience of the new approach by giving a short proof that extending adversaries to a larger class of partial algorithms with errors does not change the strength of the security assumption.

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