A Cryptanalysis on a Generalized Threshold Cryptosystem

In 1987, Desmedt first proposed a group oriented cryptosystem. During the past decade, group oriented cryptosystem has become one of the important cryptographical primitives. Laih and Harn proposed a generalized threshold cryptosystem with two models in 1991. In their system, each group is only assigned public key. A ciphertext can be decoded by utilizing all the secret keys owned by the users of any access instance. In this paper we will show that Laih-Harn’s generalized threshold cryptosystem can not withstand a cooperative attack. Their cryptosystem is insecure.