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All exceptional groups of lie type have minimal logarithmic signatures

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

As a special type of factorization of finite groups, logarithmic signature (LS) is used as the main component of cryptographic keys for secret key cryptosystems such as PGM and public key cryptosystems like \(MST_1, MST_2\) and \(MST_3\). An LS with the shortest length is called a minimal logarithmic signature (MLS) that is highly favourable to be used for cryptographic constructions. The MLS conjecture states that every finite simple group has an MLS. Recently, Nikhil Singhi et al. proved the MLS conjecture to be true for some families of simple groups. In this paper, we firstly prove the existence of MLSs for the exceptional groups of Lie type.

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Acknowledgments

This work is partially supported by the National Natural Science Foundation of China (NSFC) (Nos. 61103198, 61121061 and 61370194) and the NSFC A3 Foresight Program (No. 61161140320).

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Authors and Affiliations

  1. Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, 100876, People’s Republic of China

    Haibo Hong, Licheng Wang, Yixian Yang & Haseeb Ahmad

Authors
  1. Haibo Hong
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  2. Licheng Wang
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  3. Yixian Yang
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  4. Haseeb Ahmad
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Correspondence to Licheng Wang.

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Hong, H., Wang, L., Yang, Y. et al. All exceptional groups of lie type have minimal logarithmic signatures. AAECC 25, 287–296 (2014). https://doi.org/10.1007/s00200-014-0226-3

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  • DOI: https://doi.org/10.1007/s00200-014-0226-3

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