Selected Areas in Cryptography
Volume 2259 of the series Lecture Notes in Computer Science pp 4959
Boolean Functions with Large Distance to All Bijective Monomials: N Odd Case
 Amr YoussefAffiliated withDepartment of Combinatorics & Optimization, Center for Applied Cryptographic Research, University of Waterloo
 , Guang GongAffiliated withDepartment of Electrical and Computer Engineering, Center for Applied Cryptographic Research, University of Waterloo
Abstract
Cryptographic Boolean functions should have large distance to functions with simple algebraic description to avoid cryptanalytic attacks based on successive approximation of the round function such as the interpolation attack. Hyperbent functions achieve the maximal minimum distance to all the coordinate functions of all bijective monomials. However, this class of functions exists only for functions with even number of inputs. In this paper we provide some constructions for Boolean functions with odd number of inputs that achieve large distance to all the coordinate functions of all bijective monomials.
Key words
Boolean functions hyperbent functions extended Hadamard transform Legendre sequences nonlinearity Title
 Boolean Functions with Large Distance to All Bijective Monomials: N Odd Case
 Book Title
 Selected Areas in Cryptography
 Book Subtitle
 8th Annual International Workshop, SAC 2001 Toronto, Ontario, Canada, August 16–17, 2001 Revised Papers
 Pages
 pp 4959
 Copyright
 2001
 DOI
 10.1007/354045537X_4
 Print ISBN
 9783540430667
 Online ISBN
 9783540455370
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 2259
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
 Additional Links
 Topics
 Keywords

 Boolean functions
 hyperbent functions
 extended Hadamard transform
 Legendre sequences
 nonlinearity
 Industry Sectors
 eBook Packages
 Editors

 Serge Vaudenay ^{(4)}
 Amr M. Youssef ^{(5)}
 Editor Affiliations

 4. EPFL, LASEC
 5. University of Waterloo, CACR
 Authors

 Amr Youssef ^{(6)}
 Guang Gong ^{(7)}
 Author Affiliations

 6. Department of Combinatorics & Optimization, Center for Applied Cryptographic Research, University of Waterloo, N2L 3G1, Ontario, Waterloo, Canada
 7. Department of Electrical and Computer Engineering, Center for Applied Cryptographic Research, University of Waterloo, N2L 3G1, Ontario, Waterloo, Canada
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