Future Generation Computer Systems 20 (2004) 887–893 A nonrepudiable threshold multi-proxy multi-signature scheme with shared verification Shiang-Feng Tzeng a,∗ , Cheng-Ying Yang b , Min-Shiang Hwang c a Department of Computer Science and Information Engineering, National Central University, No. 300, Jung-da Rd., Jung-li City, 320 Taoyuan, Taiwan, ROC b Graduate Institute of Networking and Communication Engineering, Chaoyang University of Technology, 168 Gifeng E. Rd., Wufeng, 413 Taichung, Taiwan, ROC c Department of Management Information System, National Chung Hsing University, 250 Kuo Kuang Road, 402 Taichung, Taiwan, ROC Received 26 February 2003; received in revised form 5 January 2004; accepted 19 January 2004 Available online 18 March 2004 Abstract In this paper, we shall propose a threshold multi-proxy multi-signature scheme with shared verification. In the scheme allows the group of original signers to delegate the signing capability to the designated group of proxy signers. Furthermore, a subset of verifiers in the designated verifier group can authenticate the proxy signature. A threshold multi-proxy multi-signature scheme with the nonrepudiation property is a scheme where the proxy group cannot deny signing for the message and the verifier group can identify the proxy group for a proxy signature. © 2004 Elsevier B.V. All rights reserved. Keywords: Digital signature; Proxy signature; Threshold proxy signature; Proxy multi-signature scheme; Multi-proxy multi-signature scheme; Threshold multi-proxy multi-signature scheme 1. Introduction A new type of digital signature, proxy signature, was first proposed in 1996 [6,7]. The proxy signature allows a designated person, called a proxy signer, to sign on behalf of an original signer. So far, many proxy signature schemes were discussed [1,3–5,8,9,11–14]. They distinguish into several kinds of proxy sig- nature schemes. The proxy multi-signature schemes were proposed in [13]. In the proxy multi-signature schemes, a proxy signer is allowed to generate a proxy multi-signature on behalf of two or more orig- ∗ Corresponding author. E-mail address: sftzeng@csie.ncu.edu.tw (S.-F. Tzeng). inal signers. The threshold proxy signature schemes were also widely proposed [1,3–5,8,11,12,14]. In the (t,n) threshold proxy signature scheme, any t or more of the proxy singers can cooperatively sign messages on behalf of an original signer. Recently, a kind of proxy signature scheme, multi-proxy multi-signature scheme, was proposed [9]. The scheme allows the group of original signers to delegate the signing capability to the designated group of proxy signers. In the schemes mentioned above, outsiders are al- lowed to play the role of verifiers. However, in most existing signature schemes, there can be only one legal signer and one legal verifier. To bridge this gap, Hsu and Wu [2] used the concept of (t,n) threshold signa- ture to extend the capability of verification which is 0167-739X/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.future.2004.01.002