IEICE TRANSACTIONS on Fundamentals
Highly Nonlinear Vector Boolean Functions
Summary :
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.
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- IEICE TRANSACTIONS on Fundamentals Vol.E82-A No.5 pp.807-814
- Publication Date
- 1999/05/25
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- Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
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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
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@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},}
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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 -
English
