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Minimal logarithmic signatures for one type of classical groups

Content Provider	Springer Nature Link
Author	Shao, Jun Hong, Haibo Ahmad, Haseeb Yang, Yixian Wang, Licheng
Copyright Year	2016
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 $$P{\varOmega }_n(q)$$ .
Ending Page	192
Page Count	16
Starting Page	177
File Format	PDF
ISSN	09381279
e-ISSN	14320622
Journal	Applicable Algebra in Engineering, Communication and Computing
Issue Number	2
Volume Number	28
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2016-08-30
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Algebraic coding theory; cryptography Theory of Computation Projective commutator subgroup Applications to coding theory and cryptography Linear algebraic groups over finite fields (Minimal) logarithmic signature Orthogonal group Stabilizer Computer Hardware Simple groups Translation planes and spreads Combinatorial aspects of groups and algebras Artificial Intelligence (incl. Robotics) Spreads Cryptography Simple groups: alternating groups and groups of Lie type Symbolic and Algebraic Manipulation Maximal subgroups
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Algebra and Number Theory

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