Extended Abstract
Binary de Bruijn sequences of period 2n bits have the property that all 2n distinct n-tupies occur once per period. To generate such a sequence with an n-stage shift-register requires the use of nonlinear feedback. These properties suggest that de Bruijn sequences may be useful in stream ciphers. However, any binary sequence can be generated using a linear-feedback shift register (LFSR) of sufficient length. Thus, the linear complexity of a sequence, defined as the length of the shortest LFSR which generates it, is often used as a measure of the unpredictability of the sequence. This is a useful measure, since a well-known algorithm [1] can be used to successfully predict all bits of any sequence with linear complexity C from a. knowledge of 2C bits. AS an example, an m-sequence of period 2n −1 has linear complexity C=n, which clearly indicates that m-sequences are highly predictable.
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References
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© 1990 Springer-Verlag Berlin Heidelberg
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Kwok, R.T.C., Maurice, B. (1990). Aperiodic Linear Complexities of de Bruijn Sequences. In: Goldwasser, S. (eds) Advances in Cryptology — CRYPTO’ 88. CRYPTO 1988. Lecture Notes in Computer Science, vol 403. Springer, New York, NY. https://doi.org/10.1007/0-387-34799-2_33
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DOI: https://doi.org/10.1007/0-387-34799-2_33
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