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
Dalam kertas kerja ini kita mengkaji n-input m-output fungsi Boolean (singkatan (n,m)-fungsi) dengan ketaklinearan tinggi. Pertama, kami membentangkan kaedah pembinaan asas untuk keseimbangan (n,m)-fungsi berdasarkan unsur primitif dalam GF(2m). Dengan prosedur berulang, kami menambah baik beberapa sempadan bawah ketaklinieran maksimum seimbang (n,m)-fungsi. Batasan yang terhasil adalah lebih besar daripada ketaklinearan maksimum yang dicapai oleh mana-mana kaedah pembinaan sebelumnya untuk (n,m)-fungsi. Akhirnya, kaedah asas kami dibangunkan untuk membina (n,m)-fungsi bengkok dan bincangkan darjah algebra maksimumnya.
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Salinan
Takashi SATOH, Kaoru KUROSAWA, "Highly Nonlinear Vector Boolean Functions" in IEICE TRANSACTIONS on Fundamentals,
vol. E82-A, no. 5, pp. 807-814, May 1999, doi: .
Abstract: In this paper we study n-input m-output Boolean functions (abbr. (n,m)-functions) with high nonlinearity. First, we present a basic construction method for a balanced (n,m)-function based on a primitive element in GF(2m). With an iterative procedure, we improve some lower bounds of the maximum nonlinearity of balanced (n,m)-functions. The resulting bounds are larger than the maximum nonlinearity achieved by any previous construction method for (n,m)-functions. Finally, our basic method is developed to construct an (n,m)-bent function and discuss its maximum algebraic degree.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e82-a_5_807/_p
Salinan
@ARTICLE{e82-a_5_807,
author={Takashi SATOH, Kaoru KUROSAWA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Highly Nonlinear Vector Boolean Functions},
year={1999},
volume={E82-A},
number={5},
pages={807-814},
abstract={In this paper we study n-input m-output Boolean functions (abbr. (n,m)-functions) with high nonlinearity. First, we present a basic construction method for a balanced (n,m)-function based on a primitive element in GF(2m). With an iterative procedure, we improve some lower bounds of the maximum nonlinearity of balanced (n,m)-functions. The resulting bounds are larger than the maximum nonlinearity achieved by any previous construction method for (n,m)-functions. Finally, our basic method is developed to construct an (n,m)-bent function and discuss its maximum algebraic degree.},
keywords={},
doi={},
ISSN={},
month={May},}
Salinan
TY - JOUR
TI - Highly Nonlinear Vector Boolean Functions
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 807
EP - 814
AU - Takashi SATOH
AU - Kaoru KUROSAWA
PY - 1999
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E82-A
IS - 5
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - May 1999
AB - In this paper we study n-input m-output Boolean functions (abbr. (n,m)-functions) with high nonlinearity. First, we present a basic construction method for a balanced (n,m)-function based on a primitive element in GF(2m). With an iterative procedure, we improve some lower bounds of the maximum nonlinearity of balanced (n,m)-functions. The resulting bounds are larger than the maximum nonlinearity achieved by any previous construction method for (n,m)-functions. Finally, our basic method is developed to construct an (n,m)-bent function and discuss its maximum algebraic degree.
ER -