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MODIFYING MAIORANA--MCFARLAND TYPE BENT FUNCTIONS FOR GOOD CRYPTOGRAPHIC PROPERTIES AND EFFICIENT IMPLEMENTATION.

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Title: MODIFYING MAIORANA--MCFARLAND TYPE BENT FUNCTIONS FOR GOOD CRYPTOGRAPHIC PROPERTIES AND EFFICIENT IMPLEMENTATION.
Authors: DENG TANG1 dtang@foxmail.com, KAVUT, SELÇUK2 skavut@balikesir.edu.tr, MANDAL, BIMAL3 bimalmandal90@gmail.com, MAITRA, SUBHAMOY4 subho@isical.ac.in
Source: SIAM Journal on Discrete Mathematics. 2019, Vol. 33 Issue 1, p238-256. 19p.
Subjects: Bent functions, Institute of Electrical & Electronics Engineers, Boolean functions, Vector valued functions, Vector spaces, Finite fields
Abstract: Very recently, a class of cryptographically significant Boolean functions were constructed by Tang and Maitra [IEEE Trans. Inform. Theory, 64 (2018), pp. 393--402] by modifying the PSap class of bent functions. The basic ideas used in Tang--Maitra construction were derived from a modification of a subclass of bent functions which is defined over the finite field, and a concern was raised in the same paper whether the implementation of such functions will be as efficient as that of Maiorana--McFarland type bent functions. In this paper, we look at the concrete realization of such functions over a vector space and answer the question positively. The first part of this paper investigates how the finite field implementation of the functions can be viewed as simple truth tables. Next, we present a completely new construction that itself starts from Maiorana--McFarland bent functions which are straightforward concatenations of linear functions. [ABSTRACT FROM AUTHOR]
Copyright of SIAM Journal on Discrete Mathematics is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: MODIFYING MAIORANA--MCFARLAND TYPE BENT FUNCTIONS FOR GOOD CRYPTOGRAPHIC PROPERTIES AND EFFICIENT IMPLEMENTATION.
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  Data: <searchLink fieldCode="DE" term="%22Bent+functions%22">Bent functions</searchLink><br /><searchLink fieldCode="DE" term="%22Institute+of+Electrical+%26+Electronics+Engineers%22">Institute of Electrical & Electronics Engineers</searchLink><br /><searchLink fieldCode="DE" term="%22Boolean+functions%22">Boolean functions</searchLink><br /><searchLink fieldCode="DE" term="%22Vector+valued+functions%22">Vector valued functions</searchLink><br /><searchLink fieldCode="DE" term="%22Vector+spaces%22">Vector spaces</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+fields%22">Finite fields</searchLink>
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  Data: Very recently, a class of cryptographically significant Boolean functions were constructed by Tang and Maitra [IEEE Trans. Inform. Theory, 64 (2018), pp. 393--402] by modifying the PSap class of bent functions. The basic ideas used in Tang--Maitra construction were derived from a modification of a subclass of bent functions which is defined over the finite field, and a concern was raised in the same paper whether the implementation of such functions will be as efficient as that of Maiorana--McFarland type bent functions. In this paper, we look at the concrete realization of such functions over a vector space and answer the question positively. The first part of this paper investigates how the finite field implementation of the functions can be viewed as simple truth tables. Next, we present a completely new construction that itself starts from Maiorana--McFarland bent functions which are straightforward concatenations of linear functions. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of SIAM Journal on Discrete Mathematics is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1137/18M1202864
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        Text: English
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        Type: general
      – SubjectFull: Institute of Electrical & Electronics Engineers
        Type: general
      – SubjectFull: Boolean functions
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      – SubjectFull: Vector valued functions
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      – SubjectFull: Vector spaces
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      – SubjectFull: Finite fields
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      – TitleFull: MODIFYING MAIORANA--MCFARLAND TYPE BENT FUNCTIONS FOR GOOD CRYPTOGRAPHIC PROPERTIES AND EFFICIENT IMPLEMENTATION.
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              Text: 2019
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