IEICE TRANSACTIONS on Fundamentals
New Results on the Boolean Functions That Can Be Expressed as the Sum of Two Bent Functions
Summary :
In this paper, we study the problem of a Boolean function can be represented as the sum of two bent functions. This problem was recently presented by N. Tokareva when studying the number of bent functions [27]. Firstly, several classes of functions, such as quadratic Boolean functions, Maiorana-MacFarland bent functions, many partial spread functions etc, are proved to be able to be represented as the sum of two bent functions. Secondly, methods to construct such functions from low dimension ones are also introduced. N. Tokareva's main hypothesis is proved for n≤6. Moreover, two hypotheses which are equivalent to N. Tokareva's main hypothesis are presented. These hypotheses may lead to new ideas or methods to solve this problem. Finally, necessary and sufficient conditions on the problem when the sum of several bent functions is again a bent function are given.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E99-A No.8 pp.1584-1590
- Publication Date
- 2016/08/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E99.A.1584
- Type of Manuscript
- PAPER
- Category
- Cryptography and Information Security
Authors
Longjiang QU
National University of Defense Technology
Shaojing FU
National University of Defense Technology,Beijing University of Posts and Telecommunications
Qingping DAI
National University of Defense Technology
Chao LI
National University of Defense Technology
Keyword
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Longjiang QU, Shaojing FU, Qingping DAI, Chao LI, "New Results on the Boolean Functions That Can Be Expressed as the Sum of Two Bent Functions" in IEICE TRANSACTIONS on Fundamentals,
vol. E99-A, no. 8, pp. 1584-1590, August 2016, doi: 10.1587/transfun.E99.A.1584.
Abstract: In this paper, we study the problem of a Boolean function can be represented as the sum of two bent functions. This problem was recently presented by N. Tokareva when studying the number of bent functions [27]. Firstly, several classes of functions, such as quadratic Boolean functions, Maiorana-MacFarland bent functions, many partial spread functions etc, are proved to be able to be represented as the sum of two bent functions. Secondly, methods to construct such functions from low dimension ones are also introduced. N. Tokareva's main hypothesis is proved for n≤6. Moreover, two hypotheses which are equivalent to N. Tokareva's main hypothesis are presented. These hypotheses may lead to new ideas or methods to solve this problem. Finally, necessary and sufficient conditions on the problem when the sum of several bent functions is again a bent function are given.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E99.A.1584/_p
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@ARTICLE{e99-a_8_1584,
author={Longjiang QU, Shaojing FU, Qingping DAI, Chao LI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={New Results on the Boolean Functions That Can Be Expressed as the Sum of Two Bent Functions},
year={2016},
volume={E99-A},
number={8},
pages={1584-1590},
abstract={In this paper, we study the problem of a Boolean function can be represented as the sum of two bent functions. This problem was recently presented by N. Tokareva when studying the number of bent functions [27]. Firstly, several classes of functions, such as quadratic Boolean functions, Maiorana-MacFarland bent functions, many partial spread functions etc, are proved to be able to be represented as the sum of two bent functions. Secondly, methods to construct such functions from low dimension ones are also introduced. N. Tokareva's main hypothesis is proved for n≤6. Moreover, two hypotheses which are equivalent to N. Tokareva's main hypothesis are presented. These hypotheses may lead to new ideas or methods to solve this problem. Finally, necessary and sufficient conditions on the problem when the sum of several bent functions is again a bent function are given.},
keywords={},
doi={10.1587/transfun.E99.A.1584},
ISSN={1745-1337},
month={August},}
Copy
TY - JOUR
TI - New Results on the Boolean Functions That Can Be Expressed as the Sum of Two Bent Functions
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1584
EP - 1590
AU - Longjiang QU
AU - Shaojing FU
AU - Qingping DAI
AU - Chao LI
PY - 2016
DO - 10.1587/transfun.E99.A.1584
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E99-A
IS - 8
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - August 2016
AB - In this paper, we study the problem of a Boolean function can be represented as the sum of two bent functions. This problem was recently presented by N. Tokareva when studying the number of bent functions [27]. Firstly, several classes of functions, such as quadratic Boolean functions, Maiorana-MacFarland bent functions, many partial spread functions etc, are proved to be able to be represented as the sum of two bent functions. Secondly, methods to construct such functions from low dimension ones are also introduced. N. Tokareva's main hypothesis is proved for n≤6. Moreover, two hypotheses which are equivalent to N. Tokareva's main hypothesis are presented. These hypotheses may lead to new ideas or methods to solve this problem. Finally, necessary and sufficient conditions on the problem when the sum of several bent functions is again a bent function are given.
ER -
English
