Open Problems on the Cross-correlation of m-Sequences
- Tor HellesethAffiliated withDepartment of Informatics, The Selmer Center, University of Bergen Email author
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.
- Open Problems on the Cross-correlation of m-Sequences
- Book Title
- Open Problems in Mathematics and Computational Science
- pp 163-179
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- Online ISBN
- Springer International Publishing
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- Springer International Publishing Switzerland
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