Improvement of an efficient ID-based RSA multisignature

In 2008, Harn and Ren proposed an effective RSA multisignature scheme based on the identity-based signature (IBS) scheme of Shamir. In spite of being a multisignature, the signature length of Harn and Ren's scheme is comparable to that in Shamir's IBS scheme. Also, only two/one extra increments of l-1 modular multiplications are added to the signature/verification time, whereby l represents the number of signers. This enabled a large reduction of computational load and communication costs compared to the multisignature schemes formerly proposed. However, we discovered two security loopholes in their schemes. The purpose of this paper is to analyze and highlight the origins of the loopholes, as well as to put forth proposed improvements, preserve the merits of the original schemes, and enhance their security. The resultant protocol thus is suitable for wireless communications because it is not only possessing security but also saving computation resources and communication bandwidth.