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The Existence of Minimal Logarithmic Signatures for Some Finite Simple Unitary Groups

Abstract

The MLS conjecture states that every finite simple group has a minimal logarithmic signature. The aim of this paper is proving the existence of a minimal logarithmic signature for some simple unitary groups PSUn(q). We report a gap in the proof of the main result of Hong et al. (Des. Codes Cryptogr. 77: 179–191, 2015) and present a new proof in some special cases of this result. As a consequence, the MLS conjecture is still open.

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Acknowledgements

We are indebted to two anonymous referees for their suggestions and helpful remarks led us to improve this paper. The research of the authors is partially supported by INSF under grant number 93010006.

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Correspondence to Ali Reza Ashrafi.

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Rahimipour, A.R., Ashrafi, A.R. The Existence of Minimal Logarithmic Signatures for Some Finite Simple Unitary Groups. Vietnam J. Math. 50, 217–227 (2022). https://doi.org/10.1007/s10013-021-00489-5

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  • DOI: https://doi.org/10.1007/s10013-021-00489-5

Keywords

  • Minimal logarithmic signature
  • Simple unitary group
  • Cryptosystem

Mathematics Subject Classification (2010)

  • 20D08
  • 94A60