NDLI: Vectorial Bent Functions From Multiple Terms Trace Functions

Content Provider	IEEE Xplore Digital Library
Author	Muratovic-Ribic, A. Pasalic, E. Bajric, S.
Copyright Year	1963
Abstract	In this paper, we provide necessary and sufficient conditions for a function of the form F(x)=Trk^2k(Σi=1^taix^ri(2k-1)) to be bent. Three equivalent statements, all of them providing both the necessary and sufficient conditions, are derived. In particular, one characterization provides an interesting link between the bentness and the evaluation of F on the cyclic group of the (2^k+1)th primitive roots of unity in GF(2^2k). More precisely, for this group of cardinality 2^k+1 given by U={u ∈ GF(2^2k):u^2k+1=1}, it is shown that the property of being vectorial bent implies that Im(F)=GF(2^k)∪{0}, if F is evaluated on U, that is, F(u) takes all possible values of GF(2^k)* exactly once and the zero value is taken twice when u ranges over U. This condition is then reformulated in terms of the evaluation of certain elementary symmetric polynomials related to F, which in turn gives some necessary conditions on the coefficients ai (for binomial trace functions) that can be stated explicitly. Finally, we show that a bent trace monomial of Dillon's type Trk^2k(λx^r(2k-1)) is never a vectorial bent function.
Sponsorship	IEEE Information Theory Society
Starting Page	1337
Ending Page	1347
Page Count	11
File Size	289142
File Format	PDF
ISSN	00189448
Volume Number	60
Issue Number	2
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2014-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Polynomials Boolean functions Cryptography Generators Transforms Information theory vectorial bent functions Binomial trace functions cryptography linearized polynomials symmetric polynomials
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

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