Minimal logarithmic signatures for one type of classical groups

Haibo Hong; Licheng Wang; Haseeb Ahmad; Jun Shao; Yixian Yang

doi:10.1007/s00200-016-0302-y

Minimal logarithmic signatures for one type of classical groups

Haibo Hong^*
, Licheng Wang
, Haseeb Ahmad
, Jun Shao
, Yixian Yang

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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 MST₁, MST₂ and MST₃. 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 PΩ_n(q).

Original language	English
Pages (from-to)	177-192
Number of pages	16
Journal	Applicable Algebra in Engineering, Communications and Computing
Volume	28
Issue number	2
DOIs	https://doi.org/10.1007/s00200-016-0302-y
Publication status	Published - 1 Mar 2017
Externally published	Yes

Keywords

(Minimal) logarithmic signature
Orthogonal group
Projective commutator subgroup
Spreads
Stabilizer

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10.1007/s00200-016-0302-y

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title = "Minimal logarithmic signatures for one type of classical groups",

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 MST1, MST2 and MST3. 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 GLn(q) , special linear groups SLn(q) , and symplectic groups Spn(q) with q a power of primes and for orthogonal groups On(q) with q a power of 2. In this paper, we present new constructions of minimal logarithmic signatures for the orthogonal group On(q) and SOn(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 PΩn(q).",

keywords = "(Minimal) logarithmic signature, Orthogonal group, Projective commutator subgroup, Spreads, Stabilizer",

author = "Haibo Hong and Licheng Wang and Haseeb Ahmad and Jun Shao and Yixian Yang",

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year = "2017",

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doi = "10.1007/s00200-016-0302-y",

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T1 - Minimal logarithmic signatures for one type of classical groups

AU - Hong, Haibo

AU - Wang, Licheng

AU - Ahmad, Haseeb

AU - Shao, Jun

AU - Yang, Yixian

PY - 2017/3/1

Y1 - 2017/3/1

N2 - 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 MST1, MST2 and MST3. 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 GLn(q) , special linear groups SLn(q) , and symplectic groups Spn(q) with q a power of primes and for orthogonal groups On(q) with q a power of 2. In this paper, we present new constructions of minimal logarithmic signatures for the orthogonal group On(q) and SOn(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 PΩn(q).

AB - 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 MST1, MST2 and MST3. 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 GLn(q) , special linear groups SLn(q) , and symplectic groups Spn(q) with q a power of primes and for orthogonal groups On(q) with q a power of 2. In this paper, we present new constructions of minimal logarithmic signatures for the orthogonal group On(q) and SOn(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 PΩn(q).

KW - (Minimal) logarithmic signature

KW - Orthogonal group

KW - Projective commutator subgroup

KW - Spreads

KW - Stabilizer

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DO - 10.1007/s00200-016-0302-y

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EP - 192

JO - Applicable Algebra in Engineering, Communications and Computing

JF - Applicable Algebra in Engineering, Communications and Computing

IS - 2

ER -

Minimal logarithmic signatures for one type of classical groups

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Keywords

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