Cryptanalysis of Modification to Self-Certified Group-Oriented Cryptosystem without A Combiner

In a (t, n) group-oriented cryptosystem collaboration of at least t participants is required to perform a designated cryptographic operation. This type of cryptographic operation is very important to support an ad-hoc type network, such as the one that is built using Bluetooth or ad-hoc wireless LAN, since the existence of a combiner is not required to decrypt an encrypted message. In the earlier paper, it was shown that a group-oriented encryption scheme, as proposed by Saeednia and Ghodosi, can be subjected to a conspiracy attack in which two participants collude to decrypt an encrypted message. Recently, it was shown that the modified scheme is subjected to a conspiracy attack of at least three group members with probability 0.608. In this paper, we show a stronger result that shows any conspiracy of at least three group members can collude and decrypt an encrypted message.