Minimal logarithmic signatures for the unitary group $$U_n(q)$$ U n ( q )

Abstract

As a special type of factorization of finite groups, logarithmic signature (LS) is used as one of the main components of the private key cryptosystem $$PGM$$PGM and the public key cryptosystems $$MST_1$$MST1, $$MST_2$$MST2 and $$MST_3$$MST3. An LS with the shortest length is called a minimal logarithmic signature (MLS) and is even desirable for cryptographic constructions. The MLS conjecture states that every finite simple group has an MLS. Recently, Singhi et al. proved that the MLS conjecture is true for some families of simple groups. In this paper, we prove the existence of MLSs for the unitary group $$U_n(q)$$Un(q) and construct MLSs for a type of simple groups--the projective special unitary group $$PSU_n(q)$$PSUn(q).