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Evaluating the Maximum Order Complexity of a Uniformly Distributed Sequence Over Odd Characteristic
2018 IEEE International Conference on Consumer Electronics-Taiwan (ICCE-TW) (2018)
  • Yuta Kodera, Graduate School of Natural Science and Technology Okayama University
  • Takuya Kusaka, Graduate School of Natural Science and Technology Okayama University
  • Takeru Miyazaki, The University of Kitakyushu
  • Yasuyuki Nogamit, Graduate School of Natural Science and Technology Okayama University
  • Satoshi Uehara, University of Kitakyushu
  • Robert H Morelos-Zaragoza, San Jose State University
Abstract
The randomness property is widely used for realizing the real communication systems. Especially for the security applications such as cryptosystems and authentication systems, it is an inseparable part of the security. A pseudorandom sequence is one of the techniques to realize the behavior of the random numbers, however, not every sequence is suitable for the security use. A random sequence needs to be evaluated from some specific properties such as the period, the bits distribution and the non-linear features.

The authors target a pseudorandom sequence for security applications called NTU sequence with a uniformization technique. The several properties of the original NTU sequence have been evaluated and been theoretically proven. On the other hand, the non-linear features of the uniformized NTU sequence still have not investigated. Therefore, to know the affects of the uniformization for the non-linearity of the original NTU sequence, this paper compares the Maximum Order Complexity (MOC) of the uniformized NTU sequence and the original one.

The experimental result claims that the MOC of the uni-formized NTU sequence is almost equivalent to the original one. However, it is experimentally found that if an odd prime p is quite small, then the difference of the MOC of two NTU sequences become large in proportion to the size of an extension degree m. Thus, a suitable parameter selection will be requited and theoretic proofs will be considered in future works.
Publication Date
August 30, 2018
Citation Information
Yuta Kodera, Takuya Kusaka, Takeru Miyazaki, Yasuyuki Nogamit, et al.. "Evaluating the Maximum Order Complexity of a Uniformly Distributed Sequence Over Odd Characteristic" 2018 IEEE International Conference on Consumer Electronics-Taiwan (ICCE-TW) (2018) ISSN: 2575-8284
Available at: http://works.bepress.com/robert_morelos-zaragoza/49/