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Explicit Criteria for Construction of Plateaued Functions

Title
Explicit Criteria for Construction of Plateaued Functions
Authors
Hyun, Jong YoonLee, JungyunLee, Yoonjin
Ewha Authors
이윤진이정연
SCOPUS Author ID
이윤진scopus; 이정연scopusscopus
Issue Date
2016
Journal Title
IEEE TRANSACTIONS ON INFORMATION THEORY
ISSN
0018-9448JCR Link1557-9654JCR Link
Citation
vol. 62, no. 12, pp. 7555 - 7565
Keywords
Plateaued functionbent functionp-ary functioncryptographic functionWalsh-Hadamard transform
Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Indexed
SCI; SCIE; SCOPUS WOS scopus
Abstract
Plateaued functions are very important cryptographic functions due to their desirable cryptographic characteristics. We find explicit criteria for the construction of p-ary r-plateaued functions with an odd prime p. We point out that 0-plateaued functions are bent functions, and so plateaued functions generalize the notion of bent functions. We first derive an explicit form for the Walsh-Hadamard transform of a p-ary r-plateaued function. We then obtain an upper bound on the degree of p-ary r-plateaued functions, and we classify p-ary (n - 1)-plateaued functions in n variables. We also obtain explicit criteria for the existence of p-ary r-plateaued functions. Accordingly, these results lead to improved bounds on the existence of p-ary bent functions.
DOI
10.1109/TIT.2016.2582217
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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