Groups -- Complexity -- Cryptology 01 (2009), No. 1, 013--031
Copyright Heldermann Verlag 2009
Generic Case Complexity and One-Way Functions
Alex D. Myasnikov
Dept. of Mathematics, Stevens Institute of Technology, Hoboken, NJ 07030, U.S.A., U.S.A.
amiasnikov@gmail.com
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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