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The existence of minimal logarithmic signatures for the sporadic Suzuki and simple Suzuki groups

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Abstract

A logarithmic signature for a finite group G is a sequence [A 1,⋯ ,A s ] of subsets of G such that every element g∈G can be uniquely written in the form g=g 1⋯g s , where g i ∈A i , 1≤i≤s. The aim of this paper is proving the existence of an MLS for the Suzuki simple groups S z(22m+1), m>1, when 22m+1+2m+1+1 or 22m+1−2m+1+1 are primes. The existence of an MLS for untwisted group G 2(4) and the sporadic Suzuki group S u z are also proved. As a consequence of our results, we prove that the simple groups

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have an MLS.

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Acknowledgments

The authors are indebted to the referees for their suggestions and helpful remarks leaded us to rearrange the paper. The research of the first and second authors are partially supported by INSF under grant number 93010006.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, University of Qom, P.O. Box 37161–46611, Qom, I.R., Iran

    A. R. Rahimipour & A. Gholami

  2. Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, 87317–51116, I.R., Iran

    A. R. Ashrafi

Authors
  1. A. R. Rahimipour
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  2. A. R. Ashrafi
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  3. A. Gholami
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Corresponding author

Correspondence to A. R. Ashrafi.

Additional information

A. R. Ashrafi holds a PhD degree at University of Kashan.

A. R. Rahimipour holds a PhD degree at University of Qom.

A. Gholami holds a PhD degree at University of Qom.

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Rahimipour, A.R., Ashrafi, A.R. & Gholami, A. The existence of minimal logarithmic signatures for the sporadic Suzuki and simple Suzuki groups. Cryptogr. Commun. 7, 535–542 (2015). https://doi.org/10.1007/s12095-015-0129-6

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  • DOI: https://doi.org/10.1007/s12095-015-0129-6

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