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Minimal logarithmic signatures for the unitary group \(U_n(q)\)

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Abstract

As a special type of factorization of finite groups, logarithmic signature (LS) is used as one of the main components of the private key cryptosystem \(PGM\) and the public key cryptosystems \(MST_1\), \(MST_2\) and \(MST_3\). An LS with the shortest length is called a minimal logarithmic signature (MLS) and is even desirable for cryptographic constructions. The MLS conjecture states that every finite simple group has an MLS. Recently, Singhi et al. proved that the MLS conjecture is true for some families of simple groups. In this paper, we prove the existence of MLSs for the unitary group \(U_n(q)\) and construct MLSs for a type of simple groups—the projective special unitary group \(PSU_n(q)\).

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Notes

  1. A Singer cyclic group is a subgroup of \(GL(V)\) that is isomorphic to the multiplicative group \(F_{q^{2n}}^{*}\) (See [2, 8]).

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Acknowledgments

This work is partially supported by the National Natural Science Foundation of China (NSFC) (Nos. 61121061, 61103198, 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

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  1. Haibo Hong
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  2. Licheng Wang
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  3. Yixian Yang
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Correspondence to Haibo Hong or Licheng Wang.

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Communicated by R. Steinwandt.

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Hong, H., Wang, L. & Yang, Y. Minimal logarithmic signatures for the unitary group \(U_n(q)\) . Des. Codes Cryptogr. 77, 179–191 (2015). https://doi.org/10.1007/s10623-014-9996-7

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