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Open Problems on the Cross-correlation of m-Sequences

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Open Problems in Mathematics and Computational Science

Abstract

Pseudorandom sequences are important for many applications in communication systems, in coding theory, and in the design of stream ciphers. Maximum-length linear sequences (or m-sequences) are popular in sequence designs due to their long period and excellent pseudorandom properties. In code-division multiple-access (CDMA) applications, there is a demand for large families of sequences having good correlation properties. The best families of sequences in these applications frequently use m-sequences in their constructions. Therefore, the problem of determining the correlation properties of m-sequences has received a lot of attention since the 1960s, and many interesting theoretical results of practical interest have been obtained. The cross-correlation of m-sequences is also related to other important problems, such as almost perfect nonlinear functions (APN) and almost bent functions (AB), and to the nonlinearity of S-boxes in many block ciphers including AES. This chapter gives an updated survey of the cross-correlation of m-sequences and describes some of the most important open problems that still remain in this area.

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References

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Acknowledgements

This research was supported by the Norwegian Research Council.

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Authors and Affiliations

  1. Department of Informatics, The Selmer Center, University of Bergen, Thormøhlensgate 55, 5008, Bergen, Norway

    Tor Helleseth

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  1. Tor Helleseth
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Correspondence to Tor Helleseth .

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  1. Dept. of Computer Science, University of California, Santa Barbara, Santa Barbara, California, USA

    Çetin Kaya Koç

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Helleseth, T. (2014). Open Problems on the Cross-correlation of m-Sequences. In: Koç, Ç. (eds) Open Problems in Mathematics and Computational Science. Springer, Cham. https://doi.org/10.1007/978-3-319-10683-0_8

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  • DOI: https://doi.org/10.1007/978-3-319-10683-0_8

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