The discrete logarithm problem modulo one: cryptanalysing the Ariffin–Abu cryptosystem

Abstract

The paper provides a cryptanalysis of the AAβ-cryptosystem recently proposed by Ariffin and Abu. The scheme is in essence a key agreement scheme whose security is based on a discrete logarithm problem in the infinite (additive) group ℝ/ℤ (the reals modulo 1). The paper breaks the AAβ-cryptosystem (in a passive adversary model) by showing that this discrete logarithm problem can be efficiently solved in practice.

Keywords

• cryptanalysis
• continued fractions
• aaβ-cryptosystem