Constructions of 1-Resilient Boolean Functions with High Nonlinearity and Good Algebraic Degree

GE Hui; SUN Yujuan; ZHUO Zepeng

doi:10.1049/cje.2020.05.011

Volume 29 Issue 4

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GE Hui, SUN Yujuan, ZHUO Zepeng, “Constructions of 1-Resilient Boolean Functions with High Nonlinearity and Good Algebraic Degree,” Chinese Journal of Electronics, vol. 29, no. 4, pp. 667-671, 2020, doi: 10.1049/cje.2020.05.011

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GE Hui, SUN Yujuan, ZHUO Zepeng, “Constructions of 1-Resilient Boolean Functions with High Nonlinearity and Good Algebraic Degree,” Chinese Journal of Electronics, vol. 29, no. 4, pp. 667-671, 2020, doi: 10.1049/cje.2020.05.011

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Constructions of 1-Resilient Boolean Functions with High Nonlinearity and Good Algebraic Degree

doi: 10.1049/cje.2020.05.011

1.
State Key Laboratory of Integrated Service Networks, Xidian University, Xi'an 710071, China;
2.
State Key Laboratory of Cryptology, Beijing 100878, China;
3.
School of Mathematical Science, Huaibei Normal University, Huaibei 235000, China

Funds: This work is supported by the National Natural Science Foundation of China (No.61972303, No.61672414).

Received Date: 2020-01-02
Rev Recd Date: 2020-04-01
Publish Date: 2020-07-10

Abstract

Abstract

Three of the most essential criteria for cryptographically strong Boolean functions are resiliency, high nonlinearity and high algebraic degree. We give a technique for constructing 1-resilient Boolean functions with high nonlinearity via modifying PS^- class bent functions. The main technique is to extend the support of bent functions in PS^- class by additionally defining two different plateaued functions on two suitably chosen subspaces. A large class of highly nonlinear 1-resilient functions which were not known earlier are obtained.
- Algebraic degree,
- Boolean function,
- Nonlinearity,
- Resiliency,
- Stream cipher

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References(24)

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