Analysis of Sun et al.’s linkability attack on some proxy blind signature schemes

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Abstract

The proxy blind signature scheme allows the designated proxy signer using the proxy secret key to generate a blind signature on behalf of the original signer. Tan et al. presented the DLP-based and ECDLP based blind signature schemes. Awasthi and Lal proposed a improved DLP-based scheme later. Recently, Sun et al. presented linkability attack on Tan et al.’s and Awasthi–Lal’s proxy blind signature schemes respectively. In this paper, we show that Sun et al.’s attack is failed and these schemes are still satisfy the unlinkability property.

Introduction

The blind signature scheme was first proposed by Chaum (1983) in Crypto’83. The security of Chaum’s scheme is based on the difficulty of integer factoring. The blind signature scheme can achieve the unforgeability property for the signer and the unlinkability for the receiver. Mambo et al. (1996) presented the proxy signature scheme to allow the designated proxy signer to sign messages on behalf of the original signer. For example, when a manager is going on a vacation, (s)he can delegate her/his secretary to sign messages on behalf of her/him. Tan et al. (2002) presented two proxy blind signature schemes to allow the proxy signer to generate a blind signature on behalf of the original signer. Awasthi and Lal (2005) showed a forgery attack on Tan et al.’s schemes and proposed a more secure proxy blind signature scheme later. Recently, Sun et al. (2005) pointed out that neither Tan et al.’s schemes nor Awasthi–Lal’s scheme satisfy the unlinkability property of the proxy blind signature scheme. In this paper, we show that Sun et al.’s linkability attack is failed and these schemes are still satisfy the unlinkability property.

Section snippets

Reviews of Tan et al.’s and Awasthi–Lal’s proxy blind signature schemes

The system parameters in the following proxy blind signature schemes are defined as follows:

    System parameters

    p, q

    two large prime numbers, where q ∣ (p − 1)

    g

    element of Zp∗ of order q

    xo, yo

    secret key and public key of the original signer respectively, where yo=gxomodp

    xp, yp

    secret key and public key of the proxy signer respectively, where yp=gxpmodp

    h( )

    a secure and public one way hash function

    ∥

    the concatenation of strings

Sun et al.’s linkability attack on some proxy blind signature schemes

In Sun et al.’s (2005) linkability attack, they pointed out that the proxy signer can record all blinded messages and use them to trace back the corresponding blind signatures. Hence, Sun et al. claimed that all Tan et al.’s schemes and Awasthi–Lal’s scheme cannot satisfy the unlinkability property of the blind signature. The details of Sun et al.’s attack are described as follows.

Analysis of Sun et al.’s linkability attack

Harn (1995) first pointed out that Camenisch et al.’s (1994) blind signature scheme is linkable. Hoster et al. (1995) showed that Harn’s claim is incorrect later. Recently, Hwang et al., 2002, Hwang et al., 2003a, Hwang et al., 2003b, Hwang et al., 2003c presented several papers to claim that several blind signature schemes are linkable. Unfortunately many cryptanalysts (Wu and Yeh, 2005, Lee and Wu, 2004, Lee and Sun, 2003, Fan, 2003) have showed that Hwang et al.’s papers are all failed

Conclusions

Recently, Sun et al. pointed out that Tan et al.’s schemes and Awasthi–Lal’s scheme cannot satisfy the unlinkability property of the proxy blind signature scheme. In this paper, we show that Sun et al.’s linkability attack is failed and these schemes are still satisfy the unlinkability property.

Acknowledgement

This work was supported in part by the Bestwise International co.

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