Another look at generic groups

Neal Koblitz; Alfred Menezes

doi:10.3934/amc.2007.1.13

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2007, Volume 1, Issue 1: 13-28. Doi: 10.3934/amc.2007.1.13

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Another look at generic groups

Neal Koblitz^1, and
Alfred Menezes^2,

1.
Department of Mathematics, Box 354350, University of Washington, Seattle, WA 98195
2.
Department of Combinatorics & Optimization, University of Waterloo, Waterloo, Ontario N2L 3G1

Received: January 31, 2006

Revised: June 30, 2006

Published: January 2007

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Abstract

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.

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Mathematics Subject Classification: 94A60, 68P25, 11T71.

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