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A survey on the applications of Niho exponents

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Abstract

The Niho exponent was introduced by Yoji Niho, who investigated the cross-correlation function between an m-sequence and its decimation sequence in 1972. Since then, Niho exponents have been used in other research areas such as in cryptography and coding theory. In this paper, we introduce some research problems related to Niho exponents and survey some recent progress in the application of Niho exponents. Some open problems in the areas of sequence design, cryptography and coding theory regarding Niho exponents are also presented.

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Acknowledgments

The authors are very grateful to the anonymous reviewers for their comments and suggestions that improved the presentation and quality of this paper. This work was supported by the National Natural Science Foundation of China (Nos. 61761166010, 61702166) and National Natural Science Foundation of Hubei Province of China (No. 2017CFB143).

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  1. Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathematics, Hubei University, Wuhan, 430062, China

    Nian Li & Xiangyong Zeng

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  1. Nian Li
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  2. Xiangyong Zeng
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Correspondence to Xiangyong Zeng.

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This paper is dedicated to celebrate Prof. Tor Helleseth’s 70 birthday.

This article is part of the Topical Collection on Special Issue: Mathematical Methods for Cryptography

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Li, N., Zeng, X. A survey on the applications of Niho exponents. Cryptogr. Commun. 11, 509–548 (2019). https://doi.org/10.1007/s12095-018-0305-6

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