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Construction of Multiple-Valued Bent Functions Using Subsets of Coefficients in GF and RMF Domains

Milo&scaron M. RADMANOVIĆ, Radomir S. STANKOVIĆ

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Summary :

Multiple-valued bent functions are functions with highest nonlinearity which makes them interesting for multiple-valued cryptography. Since the general structure of bent functions is still unknown, methods for construction of bent functions are often based on some deterministic criteria. For practical applications, it is often necessary to be able to construct a bent function that does not belong to any specific class of functions. Thus, the criteria for constructions are combined with exhaustive search over all possible functions which can be very CPU time consuming. A solution is to restrict the search space by some conditions that should be satisfied by the produced bent functions. In this paper, we proposed the construction method based on spectral subsets of multiple-valued bent functions satisfying certain appropriately formulated restrictions in Galois field (GF) and Reed-Muller-Fourier (RMF) domains. Experimental results show that the proposed method efficiently constructs ternary and quaternary bent functions by using these restrictions.

Publication
IEICE TRANSACTIONS on Information Vol.E104-D No.8 pp.1103-1110
Publication Date
2021/08/01
Publicized
2021/04/21
Online ISSN
1745-1361
DOI
10.1587/transinf.2020LOP0009
Type of Manuscript
Special Section PAPER (Special Section on Multiple-Valued Logic and VLSI Computing)
Category
Logic Design

Authors

Milo&scaron M. RADMANOVIĆ
  University of Ni&scaron
Radomir S. STANKOVIĆ
  Mathematical Institute of SASA

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