CLC number: TP309

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Received: 2004-01-20

Revision Accepted: 2004-10-29

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XIAO Qing-hua, PING Ling-di, CHEN Xiao-ping, PAN Xue-zeng. Applying two channels to vector space secret sharing based multi-signature scheme[J]. Journal of Zhejiang University Science A, 2005, 6(1): 56-62.

@article{title="Applying two channels to vector space secret sharing based multi-signature scheme",

author="XIAO Qing-hua, PING Ling-di, CHEN Xiao-ping, PAN Xue-zeng",

journal="Journal of Zhejiang University Science A",

volume="6",

number="1",

pages="56-62",

year="2005",

publisher="Zhejiang University Press & Springer",

doi="10.1631/jzus.2005.A0056"

}

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%T Applying two channels to vector space secret sharing based multi-signature scheme

%A XIAO Qing-hua

%A PING Ling-di

%A CHEN Xiao-ping

%A PAN Xue-zeng

%J Journal of Zhejiang University SCIENCE A

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%I Zhejiang University Press & Springer

%DOI 10.1631/jzus.2005.A0056

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T1 - Applying two channels to vector space secret sharing based multi-signature scheme

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A1 - PING Ling-di

A1 - CHEN Xiao-ping

A1 - PAN Xue-zeng

J0 - Journal of Zhejiang University Science A

VL - 6

IS - 1

SP - 56

EP - 62

%@ 1673-565X

Y1 - 2005

PB - Zhejiang University Press & Springer

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DOI - 10.1631/jzus.2005.A0056

**Abstract: **Secret sharing and digital signature is an important research area in information security and has wide applications in such fields as safeguarding and legal use of confidential information, secure multiparty computation and electronic commerce. But up to now, study of signature based on general vector space secret sharing is very weak. Aiming at this drawback, the authors did some research on vector space secret sharing against cheaters, and proposed an efficient but secure vector space secret sharing based multi-signature scheme, which is implemented in two channels. In this scheme, the group signature can be easily produced if an authorized subset of participants pool their secret shadows and it is impossible for them to generate a group signature if an unauthorized subset of participants pool their secret shadows. The validity of the group signature can be verified by means of verification equations. A group signature of authorized subset of participants cannot be impersonated by any other set of participants. Moreover, the suspected forgery can be traced, and the malicious participants can be detected in the scheme. None of several possible attacks can successfully break this scheme.

**
**

. INTRODUCTION

But when cheaters appear in signatures, and if we want to detect and trace them, we may need to combine these two signatures to form a new one. We call it secret sharing based multi-signature scheme (Desmedt and Frankel,

. RELATED WORKS

Most of the researches above consider only threshold structures: the system tolerates the presence of less than

Recently, in order to make the signature scheme more practical and general, Herranz et al.(

Almost all of the signature schemes mentioned above are implemented in one channel. The main contribution of this paper is to design a two-channel secure vector space traceable multi-signature scheme. Security of the signature scheme in each channel is equal to that of an independent one. Malicious users can forge the signature only if the signatures in both channels can be forged. In our designed scheme, when a faulty signature is presented, cheaters can be detected and traced easily. In terms of performance, this scheme should not be less efficient than most of solutions available (e.g., Li et al.,

. SECURE VECTOR SPACE SECRET SHARING

Let

and sends to the participant

A scheme constructed in this way is called a vector space secret sharing scheme. Let

. PROPOSED SCHEME

Let us divide our scheme into three phases: the system initialization phase, the partial signature generation and verification phase, the group signature generation and verification phase.

Additionally, suppose

and

It is worth noting here that the public keys of each participant are also regarded as his identity information. Each

Then

holds. If so, the partial signature from

Since

and then use the group public key

holds. If so, the group signature {

Since

. SECURITY ANALYSIS

Furthermore, we can check the security of our scheme by resolving the questions given by Li et al.(

Let us consider the case where two members

Table

Scheme | Type | Signing order predetermined | Signers determined in advance | Traceability property | |

Multi-signature | Harn and Kiesler (1989) |
S | Yes | Yes | No |

Okamoto (1988) |
S | No | No | No | |

Harn (1994b) |
P | No | Yes | Yes | |

Threshold multi-signature | Li et al.(1995) |
P | No | No | Yes |

Desmedt and Frankel (1992a) |
P | No | No | No | |

Vector space secret sharing based multi-signature | Proposed | P | No | No | Yes |

Distributed RSA signature for general access structure | Herranz et al.(2003) |
P | No | No | No |

. EFFICIENCY ANALYSIS

Let

Let

Considering the communication cost, in the group signature generation process, we need

Table

Scheme | Modulo multiplication | Modulo exponentiation | Inverse computation |

Li et al.(1995) |
t+2 |
t+2 |
0 |

Harn (1994a) | op | 2t+3 |
t(1 |

Desmedt and Frankel (1992a) |
t+1 |
0 | 0 |

Herranz et al.(2003) |
t |
t+3 |
0 |

Proposed | t+1 |
5 | 0 |

Obviously, our scheme is more efficient than other similar schemes in terms of verifying the group signature.

. CONCLUSION

Furthermore, this new scheme achieves good extensibility. When applying vector space secret sharing scheme proposed by Xu et al.(

Similarly, we can even extend our scheme into one that is implemented in

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