The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
다중 값 구부러진 함수는 비선형성이 가장 높은 함수이므로 다중 값 암호화에 유용합니다. 구부러진 기능의 일반적인 구조는 아직 알려지지 않았기 때문에 구부러진 기능을 구성하는 방법은 종종 일부 결정론적 기준을 기반으로 합니다. 실제 적용을 위해서는 특정 함수 클래스에 속하지 않는 구부러진 함수를 구성할 수 있어야 하는 경우가 많습니다. 따라서 구성 기준은 CPU 시간을 많이 소모할 수 있는 가능한 모든 기능에 대한 철저한 검색과 결합됩니다. 해결책은 생성된 구부러진 함수가 충족해야 하는 일부 조건으로 검색 공간을 제한하는 것입니다. 본 논문에서는 갈루아 장(GF) 및 리드-뮬러-푸리에(RMF) 영역에서 적절하게 공식화된 특정 제한 사항을 만족하는 다중 값 굽은 함수의 스펙트럼 하위 집합을 기반으로 하는 구성 방법을 제안했습니다. 실험 결과는 제안된 방법이 이러한 제한을 이용하여 3차 및 4차 굽은 함수를 효율적으로 구성함을 보여주었다.
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},}
부
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 -