Informatica

Since threshold proxy signature has been proposed, all threshold proxy signature schemes are based on the discrete logarithm problems in the modular multiplicative group which has an element g with a large prime order. Nowadays this kind of threshold proxy signature schemes become more and more complex and time-consuming for security and specific requirement. In this paper, we propose a (bilinear) pairing-based threshold proxy signature scheme with known signers, analyze its security and check the following properties the proposed scheme has: non-repudiation, unforgeability, identifiability, distinguishability, verifiability, prevention of misuse of proxy signing right, etc. Moreover, we point out that the proposed scheme is of great efficiency by comparing it with Sun’s and Hsu et al.’s scheme.

In 2001, Hsu et al. proposed a non‐repudiable threshold proxy signature with known signers. In their scheme, the proxy group cannot deny having signed the proxy signature if they did. However, Hsu et al.'s scheme is vulnerable to some attacks. A malicious original signer or malicious proxy signer can impersonate some other proxy signers to generate proxy signatures. In this article, we shall present our cryptanalysis of the Hsu et al.'s scheme. After that, we shall propose a new threshold proxy signature that can overcome the weaknesses.

Sun's nonrepudiation threshold proxy signature scheme is not secure against the collusion attack. In order to guard against the attack, Hwang et al. proposed another threshold proxy signature scheme. However, a new attack is proposed to work on both Hwang et al.'s and Sun's schemes. By executing this attack, one proxy signer and the original signer can forge any valid proxy signature. Therefore, both Hwang et al.'s scheme and Sun's scheme were insecure.

In the (t,n) proxy signature scheme, the signature, originally signed by a signer, can be signed by t or more proxy signers out of a proxy group of n members. Recently, an efficient nonrepudiable threshold proxy signature scheme with known signers was proposed by H.-M. Sun. Sun's scheme has two advantages. One is nonrepudiation. The proxy group cannot deny that having signed the proxy signature. Any verifier can identify the proxy group as a real signer. The other is identifiable signers. The verifier is able to identify the actual signers in the proxy group. Also, the signers cannot deny that having generated the proxy signature. In this article, we present a cryptanalysis of the Sun's scheme. Further, we propose a secure, nonrepudiable and known signers threshold proxy signature scheme which remedies the weakness of the Sun's scheme.