Cryptanalysing the critical group: efficiently solving Biggs's discrete logarithm problem

Abstract

Biggs has recently proposed the critical group of a certain class of finite graphs as a platform group for cryptosystems relying on the difficulty of the discrete log problem. The paper uses techniques from the theory of Picard groups on finite graphs to show that the discrete log problem can be efficiently solved in Biggs's groups. Thus this class of groups is not suitable as a platform for discrete logarithm based cryptography.

Keywords

• critical group
• discrete logarithm problem
• cryptanalysis
• chip-firing
• picard group