带身份认证的的高效量子秘密共享方案

High-efficient Quantum Secret Sharing with Identity

Certification*

SUN Ying(孙莹)1**, WEN Qiao-Yan(温巧燕) 1, ZHU Fu-Chen(朱甫臣) 2

1

School of Science, Beijing University of Posts and Telecommunications, Beijing 100876

2

National Laboratory for Modern Communications, P.O. Box 810, Chengdu 610041

**Email: 2005amanda@

We present a high-efficient quantum secret sharing (QSS) scheme with identity certification using two-particle maximum entangled pairs. The identity sequences and one-way hash functions are shared beforehand for avoiding wasting particles while establishing the shared key. And all particles are transmitted for only one time in the quantum channels. We consider that the scheme is optimal as both the intrinsic efficiency for qubits and the total efficiency approach maximum.

Key words: quantum secret sharing, quantum cryptography, identity certification PACS: 03.67.Hk, 03.67.Dd, 03.65.Ud

QSS is one of the useful tools in the cryptographic applications. Suppose Trent wants his two agents, Alice and Bob, who are at remote places to deal with his business. However Trent doubts that one of them may be dishonest and he does not know who the dishonest one is, but he knows that the number of dishonest persons is less than two. To prevent the dishonest man from destroying the business, classical cryptography provides the secret sharing scheme in which Trent splits his secret

*Supposed by the National High Technology Research and Development Program of China, Grant No. 2006AA01Z419; the National Natural Science Foundation of China, Grants Nos. 90604023, 60373059; the National Research Foundation for the Doctoral Program of Higher Education of China, Grant No. 20040013007; the National Laboratory for Modern Communications Science Foundation of China, Grant No. 9140C1101010601; the Natural Science Foundation of Beijing.

message (M T ) into two sequences (M A and M B ) and sends them to Alice and Bob, respectively. Alice and Bob can read out the message B T A M M M =⊕only when they

cooperate. In quantum information, the task can be completed by quantum secret sharing (QSS). Both classical information and quantum information can be shared with quantum mechanics. In this paper, we only consider the issue of sharing the classical secret information.

The first QSS scheme proposed by Hillery, Bužek, and Berthiaume (hereafter we refer to HBB protocol) used a three-particle entangled Greenberger-Horne-Zeilinger (GHZ) state [1]. Although this scheme elegantly showed the essence of QSS, it is hard to realize experimentally because of the inefficiency as regards the generation of a three-particle entangled state [2]. Several variations and theoretical expansions of QSS have been reported since the publication of this pioneering work [3-15]. Among them, schemes based on two-particle entangled states [3, 4, 12, 13] have better experimental feasibility with optical setups than ones based on three-particle entangled states. However, the schemes based on two-particle entangled states do not always have satisfying efficiency. In the KKI protocol [3], for example, only half of the data obtained by expensive quantum communication can be used at most. It’s meaningful enough to improve the efficiency without loss of security. In this paper, we proposed a novel QSS scheme with identity certification and one-way transmission used two-particle maximum entangled states. In this scheme, Trent shares two secret identity sequences with Alice and Bob, respectively, before they start the protocol. We repeatedly employ the identity sequences encrypted by one-way hash functions to control the measurement basis (MB). So there are no particles wasted in the random base choosing process. Furthermore, all instances are transmitted through the quantum channel only once which means fewer particles is wasted in channel noisy. In other words, we can obtain an optimal efficiency in our QSS scheme.

The paper is outlined as follows: First, we briefly review two complete orthogonal basis sets in the two-particle quantum system and the one-way hash function. Then, we give the details of the high-efficient QSS scheme with identity certification, and discuss the security of the scheme against eavesdropping. At last, we give a conclusion.