Advances in Cryptology — EUROCRYPT'98
Volume 1403 of the series Lecture Notes in Computer Science pp 319333
Towards a better understanding of onewayness: Facing linear permutations
 Alain P. HiltgenAffiliated withUBS  Corporate IT Security
Abstract
The onewayness of linear permutations, i.e., invertible linear Boolean functions F: {0,1}n → {0, 1}n, is investigated. For linear permutations with a triangular matrix description (tlinear permutations), we prove that onewayness, C(F−1)/C(F), is nontrivially upperbounded by 16√n, where C(.) denotes unrestricted circuit complexity. We also prove that this upper bound strengthens as the complexity of the inverse function increases, limiting the onewayness of tlinear permutations with C(F−1) = n2/(c log2(n)) to a constant, i.e., a value that is independent of n. Direct implications for linear and also nonlinear permutations are discussed. Moreover, and for the first time ever, a description is given about where, in the case of linear permutations, practical onewayness would have to come from, if it exists.
 Title
 Towards a better understanding of onewayness: Facing linear permutations
 Book Title
 Advances in Cryptology — EUROCRYPT'98
 Book Subtitle
 International Conference on the Theory and Application of Cryptographic Techniques Espoo, Finland, May 31 – June 4, 1998 Proceedings
 Pages
 pp 319333
 Copyright
 1998
 DOI
 10.1007/BFb0054136
 Print ISBN
 9783540645184
 Online ISBN
 9783540697954
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 1403
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
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 Editors
 Authors

 Alain P. Hiltgen ^{(1)}
 Author Affiliations

 1. UBS  Corporate IT Security, P.O. Box, CH8021, Zurich, Switzerland
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