Minimal Logarithmic Signatures for Sporadic Groups

TL;DR

This paper proves the existence of minimal logarithmic signatures for certain sporadic groups, advancing the understanding of group factorizations relevant for cryptography.

Contribution

It establishes the existence of minimal logarithmic signatures for some sporadic groups, supporting the MLS conjecture for these cases.

Findings

Proved MLS existence for specific sporadic groups

Supports the MLS conjecture in finite simple groups

Enhances cryptographic group factorization methods

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 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. Until now, the MLS conjecture has been proved true for some families of simple groups. In this paper, we will prove the existence of minimal logarithmic signatures for some sporadic groups.