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.
Milo&scaron M. RADMANOVIĆ
University of Ni&scaron
Radomir S. STANKOVIĆ
Mathematical Institute of SASA
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Milo&scaron M. RADMANOVIĆ, Radomir S. STANKOVIĆ, "Construction of Multiple-Valued Bent Functions Using Subsets of Coefficients in GF and RMF Domains" in IEICE TRANSACTIONS on Information,
vol. E104-D, no. 8, pp. 1103-1110, August 2021, doi: 10.1587/transinf.2020LOP0009.
Abstract: 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.
URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.2020LOP0009/_p
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@ARTICLE{e104-d_8_1103,
author={Milo&scaron M. RADMANOVIĆ, Radomir S. STANKOVIĆ, },
journal={IEICE TRANSACTIONS on Information},
title={Construction of Multiple-Valued Bent Functions Using Subsets of Coefficients in GF and RMF Domains},
year={2021},
volume={E104-D},
number={8},
pages={1103-1110},
abstract={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.},
keywords={},
doi={10.1587/transinf.2020LOP0009},
ISSN={1745-1361},
month={August},}
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TY - JOUR
TI - Construction of Multiple-Valued Bent Functions Using Subsets of Coefficients in GF and RMF Domains
T2 - IEICE TRANSACTIONS on Information
SP - 1103
EP - 1110
AU - Milo&scaron M. RADMANOVIĆ
AU - Radomir S. STANKOVIĆ
PY - 2021
DO - 10.1587/transinf.2020LOP0009
JO - IEICE TRANSACTIONS on Information
SN - 1745-1361
VL - E104-D
IS - 8
JA - IEICE TRANSACTIONS on Information
Y1 - August 2021
AB - 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.
ER -