Minimal Logarithmic Signatures for one type of Classical Groups

TL;DR

This paper develops new minimal logarithmic signatures for orthogonal and related classical groups, advancing cryptographic group factorization techniques and confirming the MLS conjecture for these groups.

Contribution

It introduces novel constructions of minimal logarithmic signatures for orthogonal groups over odd prime powers and for certain classical groups' projective commutator subgroups.

Findings

Constructed MLS for orthogonal groups On(q) with q odd prime powers

Extended MLS constructions to classical groups' projective commutator subgroups

Confirmed the MLS conjecture for these 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 as 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 as a power of odd primes. Furthermore, we give constructions of MLSs for a type of classical groups projective commutator subgroup.