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A more eﬃcient way to detect eavesdropping in

“ping-pong” protocol and its application to quantum

sharing of classical secret

Fei Gao

1,2

, Fen-Zhuo Guo

, Qiao-Yan Wen

, Fu-Chen Zhu

1. School of Science, Beijing University of Posts and Telecommunications,

Beijing, 100876, China

∗

2. State Key Laboratory of Integrated Services Network, Xidian University,

Xi’an, 710071, China

3. National Laboratory for Modern Communications, P.O.Box 810,

Chengdu, 610041, China

Abstract

We present a diﬀerent way to detect eavesdropping in “ping-pong” protocol [Phys.

Rev. Lett. 89, 187902 (2002)], where we make full use of the Bell states so that

the security, which can be described by the function I(d), is improved obviously. The

method we use to compare the eﬃciency among diﬀerent detect strategies is instructive

for scheme designers. Furthermore, a quantum sharing of classical secret protocol is

proposed, in which two-particle entangled state is competent for multi-party secret

sharing.

Keywords: quantum secure direct communication, quantum cryptography, entanglement,

secret sharing

∗

hzpe@sohu.com

http://www.paper.edu.cn

I. Introduction

The task of cryptography is to make secret messages intelligible only for the two legitimate

parties of the secret communication, Alice and Bob, and unreadable for other unauthorized

users such as Eve. To this end, Alice and Bob have to encrypt their secret messages using

a suitable encryption scheme. In 1917, the one-time pad cipher was invented by American

AT&T engineer Gilbert Vernam. It was later shown, by Claude Shannon, that as long as

the key is truly random, has the same length as the message, and is never reused then the

one-time pad is perfectly secure. However, there is a snag, which is called key distribution.

Although the public key cryptography can accomplish this task, it is based on computational

security. It means that if and when mathematicians or computer scientists come up with fast

and clever procedures for factoring large integers or resolving other mathematical diﬃcult

problems, the whole privacy of public-key cryptosystems could vanish overnight. Quantum

cryptography, which is based on fundamental physical principles, has been proved to b e an

eﬀective technique for secure key distribution [1–13]. It overcomes the drawbacks possessed

by conventional cryptography and the public key cryptography, and has the vast developing

prospect.

Not long ago, Bostr¨om and Felbinger presented a “ping-pong” communication proto-

col [14] which can be used both to distribute secure key and to transfer information in a

deterministic secure manner (i.e., the so-called quantum secure direct communication [15–

18]). It utilizes the property that one bit of information can be encoded in the Bell states

|Ψ

i =

√

(|01i ± |10i), which is completely unavailable to anyone who has access to only

one of the qubits. To gain information from Alice, Bob prepares two qubits in state |Ψ

He stores one qubit and sends the other one to Alice. After she received the qubit from

Bob, Alice encodes her information “1” or “0” by performing a unitary operation σ

or I.

Then she sends it back. At last, Bob can get Alice’s information by a Bell measurement.

To detect eavesdropping, Alice randomly switches the message mode to control mode. In

control mode both Alice and Bob perform a measurement on their qubits respectively, in the

basis B

= {|0i, |1i}, and then compare the results. If both results coincide, there may be

Eve in the line; otherwise, this communication continues (see Ref. [14] for details). After the

presentation of ping-pong protocol, several related studies were proposed. An eavesdropper

http://www.paper.edu.cn

Eve can eavesdrop on the information if the quantum channel is noisy [19], and this ping-

pong protocol can be attacked without eavesdropping [20]. Furthermore, the capacity of

ping-pong protocol can be improved [21] and entanglement swapping can be used to modify

this protocol against attacks without eavesdropping [22].

As we know, quantum cryptography can b e considered unconditionally secure in theory

because any eﬀective eavesdropping would be discovered by the users, which is assured by

the fundamental principles in quantum mechanics. Consequently, the users have to sample a

certain number of photons or key bits to detect eavesdropping in most quantum cryptography

protocols. An eﬃcient way to detect implies high security or economization of resource. In

this paper, we modify the strategy to detect eavesdropping in ping-pong protocol and it

follows that a better security app ears in contrast to the original one. In addition, this

scheme can be applied to quantum sharing of classical secret (or QSCS for short). The

structure of this paper is as follows: In Sec.II, we introduce the modiﬁed ping-p ong protocol,

and its security is discussed in Sec.III. Furthermore, this proto col can be generalized to QSCS

scheme (see Sec.IV), in which the above function of state |Ψ

i is used similarly. Finally, a

conclusion is given in Sec.V.

II. The modiﬁed ping-pong protocol

In this Section, we will present a modiﬁed ping-pong protocol which, as we will show, has

higher security than Bostr¨om and Felbinger’s one [14]. For simplicity, the original ping-pong

protocol will be represented as OPP, while our modiﬁed ping-pong protocol as MPP.

Let us discuss the strategy to detect eavesdropping in OPP ﬁrst. To obtain security, as

narrated in the above section, both Alice and Bob perform a local measurement on their

qubits in the basis B

. Because the two qubits are in state |Ψ

i initially, they will draw a

conclusion that Eve does not exist when their results are opposite. Obviously, it does not

make full use of the state |Ψ

i. As we know, two qubits has a four-dimensional state space

and four Bell states ( |Ψ

i =

√

(|01i ± |10i), |Φ

i =

√

(|00i ± |11i)) construct a complete

orthogonal basis of this space. In fact, |Ψ

−

i and |Ψ

i have the same property, as far as this

kind of measurement is concerned. That is, both |Ψ

−

i and |Ψ

i yield opposite results with

certainty. Therefore, any state in the form |ψi = α|Ψ

i + β|Ψ

−

i (|α|

+ |β|

= 1) can pass

http://www.paper.edu.cn

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