Paper 2015/1079

De Bruijn Sequences from Symmetric Shift Registers

Ming Li, Mingxing Wang, and Dongdai Lin

Abstract

We consider the symmetric Feedback Shift Registers (FSRs), especially a special class of symmetric FSRs (we call them scattered symmetric FSRs), and construct a large class of De Bruijn sequences from them. It is shown that, at least O(2^((n-6)(logn)/2)) De Bruijn sequences of order n can be constructed from just one n-stage scattered symmetric FSR. To generate the next bit in the De Bruijn sequence from the current state, it requires no more than 2n comparisons and n+1 FSR shifts. By further analyse the cycle structure of the scattered symmetric FSRs, other methods for constructing De Bruijn sequences are suggested.

Metadata
Available format(s)
PDF
Category
Secret-key cryptography
Publication info
Preprint. MINOR revision.
Keywords
symmetric Boolean functionfeedback shift registerDe Bruijn sequencecycle joining method.
Contact author(s)
liming @ iie ac cn
History
2015-11-06: revised
2015-11-06: received
See all versions
Short URL
https://ia.cr/2015/1079
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2015/1079,
      author = {Ming Li and Mingxing Wang and Dongdai Lin},
      title = {De Bruijn Sequences from Symmetric Shift Registers},
      howpublished = {Cryptology {ePrint} Archive, Paper 2015/1079},
      year = {2015},
      url = {https://eprint.iacr.org/2015/1079}
}
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