A Deterministic Approach to Balancedness and Run Quantification in Pseudorandom Pattern Generators

  • Amparo Fúster-Sabater
  • Pino Caballero-Gil
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3746)


An easy method of computing the number of 1’s and 0’s (balancedness) as well as the number of runs (run quantification) in the sequence obtained from a LFSR-based pseudorandom patter generator has been developed. The procedure is a deterministic alternative to the traditional application of statistical tests. The computation method allows one to check deviation of balancedness and run distribution goodness from standard values. As a straight consequence of the above procedure, simple rules to design pattern generators with adequate pseudorandomness properties are also derived.


Deterministic approach pattern generator algorithm cryptography 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bluetooth, Specifications of the Bluetooth system, Version 1.1 (February 2001), available at
  2. 2.
    Fúster-Sabater, A., García-Mochales, P.: On the Balancedness of nonlinear generators of binary sequences. Information Processing Letters 85, 111–116 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    GSM, Global Systems for Mobile Communications, available at
  4. 4.
    Golomb, S.W.: Shift Register-Sequences, Aegean Park Press, Laguna Hill (1982)Google Scholar
  5. 5.
    Grassman, W.K., Trembley, J.P.: Logic and Discrete Mathematics. Prentice-Hall, Englewood Cliffs (1996)zbMATHGoogle Scholar
  6. 6.
    Klapper, A.: Large Families of Sequences with Near Optimal Correlations and Large Linear Span. IEEE Trans. on Information Theory 42, 1241–1248 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Mange, D.: Analysis and Synthesis of Logic Systems, Artech House, INC., Norwood (1986)Google Scholar
  8. 8.
    Meier, W., Staffelbach, O.: Nonlinearity criteria for cryptographic functions. In: Quisquater, J.-J., Vandewalle, J. (eds.) EUROCRYPT 1989. LNCS, vol. 434, pp. 549–562. Springer, Heidelberg (1990)Google Scholar
  9. 9.
    Menezes, A.J., et al.: Handbook of Applied Cryptography. CRC Press, New York (1997)zbMATHGoogle Scholar
  10. 10.
    Nelson, V.P., et al.: Digital Logic Circuit Analysis and Design. Prentice-Hall International, Englewood Cliffs (1995)Google Scholar
  11. 11.
    Rueppel, R.A.: Analysis and Design of Stream Ciphers. Springer, New York (1986)zbMATHGoogle Scholar
  12. 12.
    Shparlinski, I.E.: On the Linear Complexity of the Power Generator, Design. Codes and Cryptography 23, 5–10 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Simmons, G.J. (ed.): Contemporary Cryptology: The Science of Information Integrity. IEEE Press, New York (1991)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Amparo Fúster-Sabater
    • 1
  • Pino Caballero-Gil
    • 2
  1. 1.Instituto de Física AplicadaC.S.I.C.MadridSpain
  2. 2.DEIOCUniversity of La LagunaLa Laguna, TenerifeSpain

Personalised recommendations