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WTS 2015 Conference, April 15-17, 2015, New York, NY, USA.

A Highly Efficient and Secure Shared Key for

Direct Communications Based on Quantum

Channel

Remah Alshinina, Khaled Elleithy, and Fatima Aljanobi

Department of Computer Science and Engineering

University Of Bridgeport

Bridgeport, CT 06604, USA

ralshini@my.bridgeport.edu, elleithy@bridgeport.edu, faljanob@my.bridgeport.edu

Abstract—the reported research in literature for message

transformation by a third party does not provide the necessary

efficiency and security against different attacks. The data

transmitted through the computer network must be

confidential and authenticated in advance. In this paper, we

develop and improve security of the braided single stage

quantum cryptography. This improvement is based on a novel

authentication algorithm by using signature verification

without using the three stages protocol to share the secret key

between the sender and receiver. This approach will work

against attacks such as replay and man-in-the-middle by

increasing the security as well as the over efficiency, reducing

the overhead through using three stages and increasing the

speed of the communication between two parties.

Keywords— quantum cryptography (QC), Braided Single

Stage Protocol (BSSP), Three Stages Protocol (TSP), quantum

key distribution protocol (QKD), authentication, Signature

Verification.

I. INTRODUCTION

Quantum cryptography is considered as a new field in the

domain of quantum information processing. The security of

quantum cryptography is based on the laws of physics

unlike the security in cryptographic techniques where it is

based only on mathematical assumptions. The first paper

written on the quantum cryptography was by Stephen

Wiesner in 1970 but his paper did not receive that much

attention. In 1984, a classic paper published by Charles

Bennett and Gilles Brassard received much attention about

the topic. Scientist predicted that one-day quantum computer

will be able to crack classical public key cryptography [1].

One of the quantum cryptography protocols is the one-time

pad. Using one time pad encryption will help protecting text

messages even if it is short. Mathematicians approved that

even with infinite computational power and infinite time it is

impossible to decrypt a one-time pad encrypted message [2].

The drawback of the one-time pad is that the key can only

be used once. Quantum cryptography used in classical

physics in order to solve the key distribution problem by

utilizing the behavior of a single quantum and this known as

the BB84 protocol. BB84 protocol uses single photons in

transmission where each single photon represents a quantum

bit (qubit). To calculate the Qubits value, a measurement of

photon polarization is needed[1]. Transmitting a secret key

between the sender and the receiver over a communication

channel cannot be done without the help of Quantum Key

Distribution (QKD). QKD is considered a highly secure

sharing key mechanism between two parties.

Figure 1. The Quantum Key Distribution (QKD) Model

The transmission method in key distribution system solves

the key distribution’s problem in cryptosystem as well as

features an important and unique properly. It provides a

secure communication channel between two parties (Alice

and Bob). This secure channel can detect any eavesdrop

(Eve) that is trying to gain information of the key. As shown

in Figure 1, a communication system can be implemented

which detects eavesdropping over a quantum channel (as

optical fiber or free air) if we use quantum superposition or

quantum entanglement [3].

In 2006, a new protocol in quantum cryptography known

as the three-stage protocol was proposed. The three-stage

quantum key is similar to classical commutative

cryptography. Thought, it requires a receiver to choose a

rotation basis also for the key agreement process there is a

need of two-way exchange of messages. For security

reasons, the three-stage protocol uses separate keys between

the sender and receiver. Also, the three-stage protocol was

proven to detect a man-in-the-middle attack more precisely

than the BB84[4].

In this paper, we are going to show the shared secret key

between sender and receiver through quantum channel and

combined, which consider as the most powerful protocol in

quantum cryptography so far. The braided single stage has a

precondition of sharing the initial value by using the three

stages protocol. This method will take long time to process

and requires unitary transform through three stages, which

way carry transmit overhead and less efficiency.

The rest of this paper is structured as follows: section II

presents the related work. Section III, gives an overview of

the Three-Stage Protocol (TSP), the Braided Single Stage

Protocol (BSSP) for quantum secure communication, and

trust node as centralized authority. Section IV, proposes a

new authentication based on BSS to be deployed in quantum

cryptography and the obtained results. Finally, section V,

WTS 2015 Conference, April 15-17, 2015, New York, NY, USA.

concludes the discussion of our proposed protocol and the

findings based on extensive simulation.

II.RELATED WORK

Today, cryptography has become an important technology

especially in the Internet society. Figure 3 shows a simple

cryptosystem, where the original message (plaintext)

transmitted into cipher text through using an encryption

algorithm (EA) and key. The message transforms over a

public channel that provides the adversary a chance to

intercept the message. The receiver gets the cipher text and

converts it again into plaintext by using decryption algorithm

(DA).

For many years, quantum computing has solved difficult

problems in classical computing. Quantum cryptography

provides a secure communication system to transmit data

between parties and increases the speed of computation. The

Key Distribution Center (KDC) shares the same key between

the parties who want to share the data through symmetric

encryption. The Quantum Key Distribution (QKD) is widely

used in quantum cryptography. It protects against attackers

within the network where it can detect any eavesdropping

attempt. It has been widely reported in literature that

symmetric key distribution has several limitations due to its

very design [5, 6].

As shown in Figure 2, the Quantum Key Distribution

(QKD) is used to generate and distribute a key, not to

transmit any data over the channel. The key could be used

later to encrypt and decrypt the message, which occurs over

communication channel.

Quantum Cryptography (QC) mechanisms can be

categorized in one of the following:

• Public Key System

• Private Key System

• One Time Pad System

The method uses a unique algorithm to increase the

security of the three-stage protocol through initializing a

vector between two parties. This algorithm helps to protect

the plaintext under any intrusion attempts. There is only one

way to recover the plaintext when the intruder gets the real

time access to the element during the implementation of the

protocol. The algorithm against the photon number splitting

in this case does not need any limitation for number of

photon used in transmission and easily removes it to increase

secure quantum communication. The algorithm can be use as

one time pad’s security [7-9].

The One time Pad (OTP) is used when two parties wish to

communications have to share a key called pad. This pad is a

randomly generated key and the length of the key should be

equal to the message so it can be sent [10]. Figure 4 shows a

diagram of OTP. A scenario of this method is provided in

[10].

Quantum State Generator

Decryption Algorithm

Quantum State Generator

Sender A Receiver B

Key Key

Quantum

Channel

Public

Channel

Encryption Algorithm

Figure 2. The Quantum Key Distribution (QKD)

EA plaintext

DA

Dk2 (Ek1

(M))

Key 2

(Ek2

(M))

EVE

Key 1

Message

Figure 3. Simple Cryptosystem Diagram

Plaintext

1100 XOR KEY PAD

1001

Cipher text

1010

Sender “Alice”

Plaintext

1010

XOR

KEY PAD

1001

Plaintext

1100

Recipient

“Bob”

Figure 4. The One Time Pad (OTP)

Figure 5. The BB84 Protocol

In 1984, Charles Bennet and Gilles Brassard developed

the BB84 protocol. This protocol uses a single photon

polarization states. The single photons polarize selects one

out of two conjugate basis sets, where the photon has one of

four polarization states. The BB84 protocol goes through

four steps [11]. Figure 5 shows a schematic diagram of

BB84.

III.AN OVERVIEW OF THE BRAIDED SINGLE STAGE

PROTOCOL (BSSP) FOR QUANTUM SECURE COMMUNICATION

A. Three stages Protocol

A new powerful algorithm was presented to secure is

called the three-stage protocol. This algorithm increases the

WTS 2015 Conference, April 15-17, 2015, New York, NY, USA.

security by adding another layer of security by initiating a

vector between sender and receiver. Figure 6 shows secure

transmission in the three-stage protocol [7]. The algorithm

works as follows:

1. Alice puts a message in a box and locks it with her

own lock.

2. Bob receives the box, uses his lock to put another

lock on the box, and then sends the box back to

Alice.

3. Alice received the box, unlocks it by using her

lock, and then returns the box to Bob.

4. On the last stage, the box has only Bob’s lock

which he can then unlock it and retrieve the

message inside the box.

Three-stage protocol for the above scheme can be

carried out in quantum optics. However, the scheme will not

work in optics using full beam intensity light. Therefore, a

new algorithm was applied to enhance the security of the

three-stage protocol in optics. The first time the three-stage

quantum cryptography protocol proposed was in 2006. In

order for us to secure the transmission in the three-stage

protocol, we need to use separate keys (unitary

transformations) known only to sender UA (Alice) and

receiver UB (Bob) individually in multiple exchanges of the

photons [7]. These transformations should be commutative

(UAUB = UBUA). One of three-stage protocol advantages

is that the photons can transmit in two directions between

two parties.

The scenario of the three-stage protocol as shown in Figure

7 [7].

• Alice applies the transformation UA on the information

X and sends the photons to Bob.

• Bob Applies UB on the received photons UA(X),

producing UBUA(X) and sends them back to Alice.

• Alice Applies adjoint U†A on the received photons,

converting it to UB(X) and then sends them back to

Bob.

• Bob applies U†B on the photons to get the information

X.

The three-stage protocol that is described in Figure 7 is not

secure because it can attack by a Trojan horse.

Message Message

Message Message

Alice Bob

Alice’s Lock Alice’s & Bob’s

Lock

Bob’s Lock

Figure 6. The Process of Three Stages Protocol [7]

U†A

UA

Alice Bob

UB(X)

X

X

U†B

Alice

UA (X)

UA UB(X)

Bob

UB

Figure 7. The Three-Stage Protocol

A.1 Trojan horse attack

At a different wavelength, Eve can insert photons in the

optical channel at any stage and in a known state of

polarization. At the next stage, if Eve received the inserted

the photons then she can know the angle of polarization for

the photons that were transmitted between (Alice) and

(Bob). If the wavelength of the Trojan horse beam injected

by Eve was different from that beam on the channel, then

Eve cannot know the inserted photons between Alice and

Bob because the photon detectors are tuned to specific

wavelengths [7].

In order to enhance the security of the three-stage

protocol against any attack, a one-time pad protocol is

attached to it. The one time pad has been proven that it is

secure and hard to attack. Each bit in the plaintext is

encrypted by using a random secret key and its length is

equal to the length of the plaintext. Moreover, the cipher text

will be impossible to decrypt if the key is:

truly random,

as large as or greater than the plaintext,

never reused in whole or part, and

is kept secret

Using the one-time pad protocol has one problem,

which is the key shared between the sender and the receiver.

Attaching one time-pad with each stage of the three-stage

protocol will increase security. At the end, having three-

equation system is impossible to solve by any attacker. Also,

it will be impossible to decrypt the original message that

was sent over the channel.

In conclusion, after attaching the one time pad security at

each stage of the three-stage protocol, the new algorithm

become immune against the photon number splitting, man-

in-the-middle, and known plain text attacks [7].

B. Braided Single Stage Protocol(BSSP)

The Braided Single Stage Protocol (BSSP) for quantum

secure communication system is used to transmit data over

long distances through using a multi-photon tolerant. The

BSSP reduces the number of stages and increase the security

during the transmission of qubits [12]. The scenario of

BSSP according to [12] works as follows.

WTS 2015 Conference, April 15-17, 2015, New York, NY, USA.

• Alice’s and Bob’s must share a secret initial value

through using the three stages protocol as shown in

Figure 8.

• Alice will form the unitary transform

=

• Bob can calculate after get all the information

about

• Alice transfers k bits of information over secure

channel after applying unitary transform to Bob.

• Bob applies to receive information sent by

Alice to recover k bits of information. The State X

is initial (initial values) as shown in Figure 9.

• Both sender (Alice) and receiver (Bob) use the last

4 bits and from k-n bits to k bits to generate a new

angel with mutual agreement.

• By using the formula below, the sender and

receiver convert the last n bits to integer value.

N=

C. Trust Node as Centralized Authority

As shown in Figure 10 the scenario of Authentication

Steps [13].

• Sender wishes to communicate with receiver so it

generates a request message with its signature,

which is encrypted through its quantum channel for

verification to receiver by using QC.

• The receiver will receive the request and verifies

the signature, which is decrypted by using the

public key and trust authority.

• Receiver sends back the message with its signature

to sender.

• Sender verifies it and sends the quantum basis

through QC.

• Receiver verifies QC with basis stored, if they

match then the sender and receiver start sharing the

secret key.

Sender “Alice” Three Stages

Protocol Receiver “Bob”

X= Ɵ

initial

X= Ɵ

initial

State X

U†B

UB

U†A

Alice R(Ɵ) Bob R(Ɵ)

UA (X)

Alice R( - Ɵ) Bob R(- Ɵ)

U†A UB

UA(X)

State X

UA

Figure 8. The Sender and Receiver Shared Initial Value

Alice Bob

Information

K bits

Derived

UA UA (X) U†A

Information

K bits

Figure 9. Braided Protocol after Sharing Initial Value

Sender Receiver

Node Authority

Quantum

Channel

A Signature with Random Bits

Signature

Figure 10. Authentication Steps

IV.PROPOSED PROTOCOL

A. PROPOSED ALGORITHM

In this paper, we propose a new type of secret key

sharing schemes between the sender and receiver to encrypt

quantum information and send it through an efficient

quantum channel. The proposed scenario is described below.

I. Classical Channel Steps

1. Sender (Alice), wishes to communicate with

receiver (Bob), generates a request message with its

public key and to a third party, (assume it

is a trust authority The requested message is

encrypted by using sender private key and the

third party public key then send it to trust third

party which trusted between Alice and Bob through

classical channel as indicated in equations (1), (2),

and (3).

2. The third party will decrypt the request message

after verifies it by using the sender public key

and the Trust Authority private key as

indicated in equation (4).

3. The Trust Authority sends back the message with

its signature and shares the secret key with the

sender and the receiver.

4. The Trust Authority sends the request message that

it got from Alice, Bob ID, and the same shared

WTS 2015 Conference, April 15-17, 2015, New York, NY, USA.

secret key then encrypts it by using Bob public key

and Trust Authority private key.

5. Now the sender and the receiver share the same

secret key as a binary number. The secret key will

be generated randomly for each session to ensure

its security and efficiency.

6. The decryption process would be the inverse of the

previous steps.

II. Quantum Channel Steps

1. The sender converts the binary secret key and

represents it as quantum key (state vector) through

the function phi = bin2vec (bin).

2. Apply the Pretty Printed function as pretty (psi) to

represent superposition state (state vector psi).

3. Apply the unitary matrix as shown in equation (5)

in parallel to represent the function as U_f=uf (f, m,

n) where x is the bit string, m is the input, and n is

the output bits. Function (f) should be in the form

of f (x, n) and do unitary matrix from f.

4. Apply the Hadamard transform (reversible gate) to

returns the n-qubits where the Hadamard matrix

implemented as H = Hadamard (n). We applied

(4*4) Hadamard (H4) to encrypt the secret key as

indicated in (6&7).

5. To get the psi before measurement, we have to

apply H*U_f*H*psi and get psi after the

measurement by using psi = measure (psi).

6. Now the secret key is represented as qubits and

Alice applies her key to transmit K bits of

information (message) over a quantum channel.

7. Bob applies the measurement step to know if he got

the same message and shared secret key from

Alice. If so, he will accept the message as shown in

Table (1). If the message and the key has been read

by Ave, the qubits collapses and Bob will get a

different qubits measurement, he will then reject

the message as shown in Table (2).

B. RESULTS

The exciting quantum cryptographic device provides

securing message authentication over quantum (optical)

channel and the public channel (third Party). The classical

cryptography mechanism uses either the shared secret

(symmetric) key between two parties who wish to share the

data or by using digital signature to produce the

authentication to protect superposition of states and quantum

states from any alter or forgery attack effectively. Applying

Hadamard matrix to determine any changes from basis to

another one.

Based on our implemented in MATLAB simulator using

QCF library as indicate in Table 1 and 2, we could provide

secure communication between the sender and receiver

through the quantum channel. The Hadamard quantum gate

and unitary function have been used. This method can

perform the encryption and decryption processes in QC and

the proposed braided single stage protocol increasing the

time of communication by using the proposed protocol is

secure against the man-in-the-middle attack and

eavesdropping by using the secret key encrypted through

quantum to increase the security and speed of the

communication between sender and receiver instead use of

the three stage protocol to share the initial values.

Equations: Commination Formulas

A complex matrix is called unitary if:

(5)

The Hadamard Transform (6)

The basis vector of the Hadamard transform take only

the binary value which is suite for digital signal

processing. Hadamard transform matrix is defined as:

Hadamard Matrix Proof (7)

A Hadamard matrix is an matrix of order

if the entries of are either or and ,

where is the transpose of and is the order identity

matrix. If H is a Hadamard matrix of order n, then:

TABLE 1: SIMULATION RESULT FROM MATLAB (ACCEPTED

MESSAGE)

Alice Public Key

Bob Public Key

Share Serest Key

(Qubits)

Unitary Matrix

Hadamard

Qubits Before

Measurement

Qubits After

Measurement

WTS 2015 Conference, April 15-17, 2015, New York, NY, USA.

TABLE 2: SIMULATION RESULT FROM MATLAB (REJECTED

MESSAGE)

Alice Public Key

Bob Public Key

Share Serest Key

(Qubits)

Unitary Matrix

Hadamard

Qubits Before

Measurement

Qubits After

Measurement

V. CONCLUSION

A novel secure node signature verification algorithm

based on the braided single stage protocol that can improve

the performance of cryptography mechanism is introduced

in this paper. Extensive simulation in MATLAB had

demonstrated that the algorithm has secured long distance

communications over quantum channels. The signature

verification provides a method to reach data integrity and

source authentication during the transmission of the secret

key by using Trust Mode as a bridge between two parties. In

this case, there is no need for the three-stage protocol to

share the initial value between sender and receiver. Thus,

the communication (or transmission) time has been

significantly reduced and the overall performance of the

system is improved. In the implementation of the quantum

key distribution protocol, the security of each stage of the

protocol is based on each party using the same key. This

technique will have a trusted node between the two parties

that should authenticate each other before exchanging

messages. The sender and receiver verify the shared secret

key then communicate through quantum channel, which can

easily detect any error, or tampering that might happen

during exchanging the message. The proposed protocol in

this paper has improved the security of the Quantum key

exchange as well as significantly enhanced the overall

performance.

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