Minimal Logarithmic Signatures for one type of Classical Groups
This work addresses a cryptographic key design problem for secret and public key cryptosystems, providing incremental advances by extending MLS constructions to previously uncovered groups.
The paper tackles the problem of constructing minimal logarithmic signatures (MLS) for orthogonal groups and related classical groups over odd prime powers, extending previous results that covered even prime powers and other groups, and presents new explicit constructions for these cases.
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.