Abstract
In applications, such as radar ranging or test pattern generation, linear recurring sequences are needed at rates that require a parallel generation of the sequences. Two parallelisation methods for the generation of these sequences are discussed and previous results are made applicable to arbitrary degrees of parallelisation and arbitrary sequences. In particular, a previously known technique (sometimes called windmill technique) is shown to be explainable in a very simple way and to be equally appropriate for the parallelisation of non-linear recursions. The method is, furthermore, shown to be suitable for VLSI-realisations and software implementations.
Chapter PDF
References
W.M. Siebert, “A Radar Detection Philosophy,” IRE Trans. Inform. Theory, vol. IT-2, pp. 204–221, (1956).
R.L. Pickholtz, D.L. Schilling, L.B. Milstein, “Theory of Spread-Spectrum Communications-A Tutorial,” IEEE Trans. Commun., vol. COM-30, pp. 855–884, May 1982.
P.H. Bardell, W.H. McAnney, “Pseudorandom Arrays for Built-In Tests,” IEEE Trans. Comput., vol. C-35, pp. 653–658, July 1986.
R.A. Rueppel, Analysis and Design of Stream Ciphers, Springer-Verlag, Berlin, Heidelberg 1986.
T. Kasami, “A Decoding Procedure for Multiple-Error-Correcting Cyclic Codes,” IEEE Trans. Inform. Theory, vol. IT-10, pp. 134–138, April 1964.
W.G. Chambers, S.M. Jennings, “Linear Equivalence of Certain BRM Shift-Register Sequences,” Electron. Lett., vol. 20, pp. 1018–1019, Nov. 1984.
A. Lempel, W.L. Eastman, “High Speed Generation of Maximal Length Sequences,” IEEE Trans. Comput., vol. C-20, pp. 227–229, Feb. 1971.
K.H. Möhrmann, “Erzeugung von binären Quasi-Zufallsfolgen hoher Taktfrequenz durch Multiplexen,” Siemens Forsch.-u. Entwickl.-Ber., vol. 3, pp. 218–224 (1974).
R. Eier, H. Malleck, “Anwendung von Multiplextechniken bei der Erzeugung von schnellen Pseudozufallsfolgen,” NTZ, vol. 28, pp. 227–231 (1975).
F. Surböck, H. Weinrichter, “Interlacing Properties of Shift-Register Sequences with Generator Polynomials Irreducible over GF(p),” IEEE Trans. Inform. Theory, vol. IT-24, pp. 386–389, May 1978.
C.F. Woodcock, P.A. Davies, “The Generation of High-Speed Binary Sequences from Interleaved Low-Speed Sequences,” IEEE Trans. Commun., vol. COM-35, pp. 115–117, Jan. 1987.
M.Y. Hsiao, “Generating PN Sequences in Parallel,” Proc., 3rd. Ann. Princeton Conf. Inform. Sci. Syst., Princeton NJ., pp. 397–401, March 1969.
W.J. Hurd, “Efficient Generation of Statistically Good Pseudonoise by Linear Interconnected Shift Registers,” IEEE Trans. Comput., vol. C-23, pp. 146–152, Feb. 1974.
D.G. Maritsas, A.C. Arvillias, A.C. Bounas, “Phase-Shift Analysis of Linear Feedback Shift Register Structures Generating Pseudorandom Sequences,” IEEE Trans. Comput., vol. C-27, pp. 660–668, July 1978.
W.W. Warlick Jr., J.E. Hershey, “High-Speed M-Sequence Generators,” IEEE Trans. Comput., vol. C-29, pp. 398–400, May 1980.
B.J.M. Smeets, Some Results on Linear Recurring Sequences, Ph.D. Thesis, Technical University of Lund, Sweden (1987).
B.J.M. Smeets, W.G. Chambers, “Windmill Generators: A Generalization and an Observation of How Many There Are,” Advances in Cryptology — EUROCRYPT’88, Lect. Notes in Comp. Science, vol. 330, pp. 325–330, Springer-Verlag (1988).
N. Zierler, “Linear Recurring Sequences,” J. Soc. Indust. Appl. Math., vol. 7, pp. 31–48, March 1959.
P.F. Duvall, J.C. Mortick, “Decimation of Periodic Sequences,” SIAM J. Appl. Math., vol. 21, pp. 367–372, Nov. 1971.
H. Niederreiter, “A Simple and General Approach to the Decimation of Feedback Shift-Register Sequences,” Probl. of Control and Inform. Theory, vol. 17, pp. 327–331 (1988).
R.G. Swan, “Factorization of Polynomials over Finite Fields,” Pac. J. Math., vol. 12, pp. 1099–1106 (1962).
L.M. Milne-Thomson, The Calculus of Finite Differences, Macmillan and Co., London 1951.
M. Ward, “The Arithmetical Theory of Linear Recurring Series,” Trans. Am. Math. Soc., vol. 35, pp. 600–628, Jan. 1933.
E.L. Key, “An Analysis of the Structure and Complexity of Nonlinear Binary Sequence Generators,” IEEE Trans. Inform. Theory, vol. IT-22, pp. 732–736, Nov. 1976.
T. Herlestam, “On Functions of Linear Shift Register Sequences,” Advances in Cryptology — EUROCRYPT’85, Lect. Notes in Comp. Science, vol. 219, pp. 119–129, Springer-Verlag (1986).
H. Hasse, “Theorie der höheren Differentiale in einem algebraischen Funktionenkörper mit vollkommenem Konstantenkörper bei beliebiger Characteristik,” J. reine angew. Math., vol. 175, pp. 50–54 (1936).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Günther, C.G. (1990). Parallel Generation of Recurring Sequences. In: Quisquater, JJ., Vandewalle, J. (eds) Advances in Cryptology — EUROCRYPT ’89. EUROCRYPT 1989. Lecture Notes in Computer Science, vol 434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46885-4_49
Download citation
DOI: https://doi.org/10.1007/3-540-46885-4_49
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-53433-4
Online ISBN: 978-3-540-46885-1
eBook Packages: Springer Book Archive