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, called a minimal logarithmic signature (MLS), is even desirable for cryptographic applications. The MLS conjecture states that every finite simple group has an MLS. Recently, the conjecture has been shown to be true for general linear groups \(GL_n(q)\), special linear groups \(SL_n(q)\), and symplectic groups \(Sp_n(q)\) with q a power of primes and for orthogonal groups \(O_n(q)\) with q a power of 2. In this paper, we present new constructions of minimal logarithmic signatures for the orthogonal group \(O_n(q)\) and \(SO_n(q)\) with q a power of an odd prime. Furthermore, we give constructions of MLSs for a type of classical groups—the projective commutator subgroup \(P{\varOmega }_n(q)\).
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Acknowledgments
This work is partially supported by the National Natural Science Foundation of China (NSFC) (Nos. 61602408,61502048,61370194), Open Foundation of State key Laboratory of Networking and Switching Technology (Beijing University of Posts and Telecommunications) (SKLNST-2016-1-05) and the NSFC A3 Foresight Program (No. 61411146001)
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Hong, H., Wang, L., Ahmad, H. et al. Minimal logarithmic signatures for one type of classical groups. AAECC 28, 177–192 (2017). https://doi.org/10.1007/s00200-016-0302-y
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DOI: https://doi.org/10.1007/s00200-016-0302-y