The existence of minimal logarithmic signatures for the sporadic Suzuki and simple Suzuki groups

Rahimipour, Ali Reza; Ашрафи, Али Реза; Gholami, Ahmad

doi:10.1007/s12095-015-0129-6

Cited by 6 publications

(2 citation statements)

References 16 publications

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“…By [4], the simple unitary group P SU 3 (5) has MLS. On the other hand, by Theorem 4.1 the unitary group P SU 4 (5) and by Theorem 4.3(2) the simple groups P SU 3 (9), P SU 3 (13) and P SU 3 (25) have MLS. Therefore, the existence of an MLS for eight simple unitary groups of order ≤ 10 12 is not still solved.…”

Section: Existence Of Mls For Some Unitary Simple Groupsmentioning

confidence: 99%

“…≤ 10 12 . These are P SU 3 (9), P SU 3 (13), P SU 3 (17), P SU 4 (5), P SU 3 (19), P SU 3 (23), P SU 3 (25), P SU 3 (29), P SU 5 (3), P SU 3 (27), P SU 3 (32) and P SU 3 (31). In this paper, it is shown that the proof of the main result of [10] regarding to existence of an MLS for projective special unitary groups is not correct and so the existence of an MLS for these groups have to be checked.…”

Section: Existence Of Mls For Some Unitary Simple Groupsmentioning

confidence: 99%

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The Existence of Minimal Logarithmic Signatures for Some Finite Simple Groups

Rahimipour

Ashrafi

Gholami

2016

Experimental Mathematics

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The M LS conjecture states that every finite simple group has a minimal logarithmic signature. The aim of this paper is proving the existence of a minimal logarithmic signature for some simple unitary groups P SU n (q). We report a gap in the proof of the main result of [H. Hong, L. Wang, Y. Yang, Minimal logarithmic signatures for the unitary group U n (q), Des. Codes Cryptogr. 77 (1) (2015) [179][180][181][182][183][184][185][186][187][188][189][190][191] and present a new proof in some special cases of this result. As a consequence, the M LS conjecture is still open.

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Section: Existence Of Mls For Some Unitary Simple Groupsmentioning

confidence: 99%

Section: Existence Of Mls For Some Unitary Simple Groupsmentioning

confidence: 99%

The Existence of Minimal Logarithmic Signatures for Some Finite Simple Groups

Rahimipour

Ashrafi

Gholami

2016

Experimental Mathematics

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Minimal logarithmic signatures for one type of classical groups

Hong

Wang

Ahmad

et al. 2016

AAECC

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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 M ST 1 , M ST 2 and M ST 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 as 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 as a power of odd primes. Furthermore, we give constructions of MLSs for a type of classical groups -projective commutator subgroup P Ω n (q).

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The Existence of Minimal Logarithmic Signatures for Some Finite Simple Unitary Groups

Rahimipour

Ashrafi

2021

Vietnam J. Math.

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The existence of minimal logarithmic signatures for the sporadic Suzuki and simple Suzuki groups

Cited by 6 publications

References 16 publications

The Existence of Minimal Logarithmic Signatures for Some Finite Simple Groups

The Existence of Minimal Logarithmic Signatures for Some Finite Simple Groups

Minimal logarithmic signatures for one type of classical groups

The Existence of Minimal Logarithmic Signatures for Some Finite Simple Unitary Groups

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