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.

A proxy signature scheme enables an original signer to delegate its signing capability to a proxy signer and then the proxy signer can sign a message on behalf of the original signer. Recently, in order to eliminate the use of certificates in certified public key cryptography and the key-escrow problem in identity-based cryptography, the notion of certificateless public key cryptography was introduced. In this paper, we first present a security model for certificateless proxy signature schemes, and then propose an efficient construction based on bilinear pairings. The security of the proposed scheme can be proved to be equivalent to the computational Diffie–Hellman problem in the random oracle with a tight reduction.

Delegation of rights is a common practice in the real world. We present two identity-based threshold proxy signature schemes, which allow an original signer to delegate her signing capability to a group of n proxy signers, and it requires a consensus of t or more proxy signers in order to generate a valid signature. In addition to identity-based scheme, privacy protection for proxy singers and security assurance are two distinct features of this work. Our first scheme provides partial privacy protection to proxy signers such that all signers' identities are revealed, whereas none of those t participating signers is specified. On the other hand, all proxy signers remain anonymous in the second scheme. This provides a full privacy protection to all proxy signers; however, each valid signature contains a tag that allows one to trace all the participating proxy signers. Both our proposed schemes are secure against unforgeability under chosen message attack, and satisfy many other necessary conditions for proxy signature.

Recently, Chen, Chung, and Huang proposed a traceable proxy multisignature scheme based on the elliptic curve cryptosystem. However, this paper shows that the original signers can produce a valid signature as the proxy signer does in the proxy protected scheme. Therefore, Chen et al.'s proxy-protected scheme cannot protect the proxy signer from being forged by the original signers. We further find that the early work of Chen et al. in 2003 suffers the same attack. To overcome this problem, an improved scheme will be presented.

A proxy signature allows a designated person, called a proxy signer, to sign the message on behalf of the original signer. Proxy signatures are very useful tools when one needs to delegate his/her signing capability to other party. A number of proxy signature schemes have been proposed and succeeded for proxy delegations, but the schemes are in defective in proxy revocations. In this paper, we propose two proxy signature schemes based on RSA cryptosystems. The proposed first scheme does not consider proxy revocation mechanism; however, it will help us to compare our protocol with the existing RSA‐based schemes. The proposed second scheme provides an effective proxy revocation mechanism. The proposed schemes do not require any secure channel to proxy key delivery and support the necessary security requirements of proxy signature.

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.