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February  2007, 1(1): 13-28. doi: 10.3934/amc.2007.1.13

Another look at generic groups

Neal Koblitz 1, and  Alfred Menezes 2,

1. 

Department of Mathematics, Box 354350, University of Washington, Seattle, WA 98195, United States
2. 

Department of Combinatorics & Optimization, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada

Received  February 2006 Revised  July 2006 Published  January 2007

Starting with Shoup's seminal paper [24], the generic group model has been an important tool in reductionist security arguments. After an informal explanation of this model and Shoup's theorem, we discuss the danger of flaws in proofs. We next describe an ontological difference between the generic group assumption and the random oracle model for hash unctions. We then examine some criticisms that have been leveled at the generic group model and raise some questions of our own.
Keywords: Cryptography, generic group., public key.
Mathematics Subject Classification: 94A60, 68P25, 11T7.
Citation: Neal Koblitz, Alfred Menezes. Another look at generic groups. Advances in Mathematics of Communications, 2007, 1 (1) : 13-28. doi: 10.3934/amc.2007.1.13
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