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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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