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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 416137, 13 pages
http://dx.doi.org/10.1155/2012/416137
Research Article

On the Security of Some Aggregate Signature Schemes

School of Computer Science and Software, Tianjin Polytechnic University, Tianjin 300387, China

Received 11 September 2012; Revised 22 November 2012; Accepted 6 December 2012

Academic Editor: Tak-Wah Lam

Copyright © 2012 Baoyuan Kang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Aggregate signature scheme proposed by Boneh, Gentry, Lynn, and Shacham allows n signatures on n distinct messages from n distinct users to aggregate a single signature that convince any verifier that n users did indeed sign the n messages, respectively. The main benefit of such schemes is that they allow bandwidth and computational savings. In this paper, we question about whether the existing aggregate signature schemes satisfy the basic property that they can convince any verifier that every user indeed signed the message which should be signed by him. We show that Rückert et al.’s scheme, and Shim’s scheme do not satisfy the property. As a comparison, we investigate Boneh et al.’s scheme and show that under the assumption that each signer correctly signs one message, Boneh et al.’s scheme satisfies this property under two users' setting. Furthermore, we propose the concept of inside attack on aggregate signatures and give an improved aggregate signature scheme based on Shim’s scheme. We also prove that the improved scheme is secure against inside attack.