All exceptional groups of lie type have minimal logarithmic signatures

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 $$MST_1, MST_2$$ M S T 1 , M S T 2 and $$MST_3$$ M S T 3 . An LS with the shortest length is called a minimal logarithmic signature (MLS) that is highly favourable to be used for cryptographic constructions. The MLS conjecture states that every finite simple group has an MLS. Recently, Nikhil Singhi et al. proved the MLS conjecture to be true for some families of simple groups. In this paper, we firstly prove the existence of MLSs for the exceptional groups of Lie type.