3. Concluding remarks
Under the correct assumptions cascading of primitive shift registers leads to interesting results. But from Gollmann’s work it is clear that general results on cascaded arbitrary shift registers cannot be expected.
In order to guarantee a good statistical behaviour of the Stop-and-Go-Sequence it is suggested that the output sequence ut is finally XOR-gated with another PN-sequence.
The statistical behaviour of (ut)t itself — though theoretically quite good in special cases — is so that a cryptoanalytic attackwould be promising in spite of the extremely high linear equivalent of the sequence.
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4. References
Beker/ Piper: Cipher Systems, Northwood 1982
Beth: Stream Ciphers, in: Secure Digital Communications, G. Longo ed., Springer 1983
Gollmann: Doctoral Dissertation, University of Linz, Austria 1983
Golomb: Shift register sequences, Holden-Day 1967
Jennings: Multiplexed Sequences, in: Cryptography, T. Beth ed., Springer LNCS 149, 1983
Selmer: Linear Recurrence Relations over Finite Fields, manuscript. Dept. of Math., University of Bergen, Norway 1960
Vogel: On the linear complexity of cascaded sequences, preprint, SEL Pforzheim, CP/ERMF, Germany 1984
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Beth, T., Piper, F.C. (1985). The Stop-and-Go-Generator. In: Beth, T., Cot, N., Ingemarsson, I. (eds) Advances in Cryptology. EUROCRYPT 1984. Lecture Notes in Computer Science, vol 209. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-39757-4_9
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