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An Efficient Algorithm for Software Generation of Binary Linear Recurrences

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract.

We describe a method for efficient software generation of binary linear sequences. Suppose that a machine sized word can hold an unsigned integer between 0 and 2w−1 and a binary linear sequence (s(t)) t ≥0 has a characteristic polynomial of degree n having l nonzero coefficients. Then given nw initial bits of the sequence, it is possible to generate successive blocks of (s(t)) t ≥0 of length w bits each. The time required to generate each block is equal to the time required to perform l bitwise XOR operations on machine sized words. Compared to the basic method of sequence generation, this provides a w-fold increase in speed.

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References

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Authors and Affiliations

  1. Centre for Artificial Intelligence and Robotics, Raj Bhavan Circle, High Grounds, Bangalore, 560 001, India

    Sanjay Burman

  2. Cryptology Research Group, Applied Statistics Unit, Indian Statistical Institute, 203, B.T. Road, Kolkata, 700 108, India

    Palash Sarkar

Authors
  1. Sanjay Burman
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  2. Palash Sarkar
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Corresponding author

Correspondence to Sanjay Burman.

Additional information

Acknowledgement We would like to thank Subhamoy Maitra, Sandeepan Choudhury and Kishan Chand Gupta for discussions and helpful comments. We would also like to thank Professor Harald Niederreiter for pointing out that Lemma 2 can be easily derived from Corollary 1 of [4]. Finally, we thank the reviewers for pointing out several typos in the paper.

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Burman, S., Sarkar, P. An Efficient Algorithm for Software Generation of Binary Linear Recurrences. AAECC 15, 201–203 (2004). https://doi.org/10.1007/s00200-004-0147-7

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  • DOI: https://doi.org/10.1007/s00200-004-0147-7

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