Quantum Key Distribution by Using Public Key Algorithm(RSA)

Abstract

Classical cryptography is based on the computational difficulty to compute the secret key using the current computing systems. Depending only on the difficulty of computational complexity does not provide enough security because finding a fast method to calculate the secret key will compromise the security of the systems. Quantum computing uses the law of physics for communication allowing new concepts to be applied in computing specially in cryptography and key distribution by applying quantum theorems and principles. In this paper, we are introducing a new model for quantum key distribution between three parties or more where there is a trusted center providing the clients the necessary secret information to securely communicate with each other.

Full text

Quantum Key Distribution by Using Public Key
Algorithm(RSA)
Ammar Odeh, Khaled Elleithy, Muneer Alshowkan, Eman Abdelfattah
Department of Computer Science & Engineering
University of Bridgeport
Bridgeport, USA
{aodeh, elleithy, malshowk, eman} @bridgeport.edu
Abstract— Classical cryptography is based on the
computational difficulty to compute the secret key using the
current computing systems. Depending only on the difficulty of
computational complexity does not provide enough security
because finding a fast method to calculate the secret key will
compromise the security of the systems. Quantum computing
uses the law of physics for communication allowing new
concepts to be applied in computing specially in cryptography
and key distribution by applying quantum theorems and
principles. In this paper, we are introducing a new model for
quantum key distribution between three parties or more where
there is a trusted center providing the clients the necessary
secret information to securely communicate with each other.
Keywords—Quantum Conputing, Three-party
Communication, Cryptography, Key Distribution;
I. INTRODUCTION
Quantum computing depends on quantum physics for
communication and quantum cryptography to secure the
communication between two parities. It allows two parities
to generate a key with special characteristics and use it for
secure communication between them. Quantum computing
allows the sender and the receiver to use two principles from
quantum mechanics. First, the Heisenberg uncertainty
principle and second, the no-cloning theorem [1]. These
principles provide the sender and the receiver absolute
security. In quantum computing the presence of an
eavesdropper who disturbs the communication can be
detected by the communicating parities. This property is
based on a concept in quantum mechanics which states that
measuring of a quantum state results in destroying that state.
An eavesdropper on the quantum channel could be detected
by superposition and entanglement [1-4]. Classical
cryptography doesn’t provide any properties to detect a third
party eavesdropping on the classical channel. No-cloning
theorem was proven in 1982 by Wootters and Zurek. It
states that a user cannot copy quantum channel state and
cannot duplicate the qubits without a prior knowledge of
their bases [2]. No-cloning principle makes it impossible
for an eavesdropper to listen to the quantum channel without
being detected unless this eavesdropper can perfectly predict
the sender random basis and use it to measure the qubits and
send them back to the receiver.
The rest of this paper is organized as follows. In Section II,
we briefly glance at the main security protocols over
quantum channel. In Section III, we describe our proposed
algorithm. Analysis of the proposed algorithm is presented
in Section IV. Finally, concluding remarks are offered in
Section V.
II. R
ELATED WORK
Quantum key distribution mainly depends on three
algorithms; BB84, B92, and EPR. Those protocols exchange
qubits over quantum channel and then apply probabilistic
measures to adjust the key bits sequence. BB84 uses
rectilinear and diagonal bases to pass data from sender to
receiver [5], [6]. The used bases are shown in equation (1)
B92 employs non-orthogonal bases to send qubits to the
receiving side [7], [8]. EPR uses one of the interesting
quantum properties which is entanglement to transfer data
between parties [9] . Two entangled states are shown in
equation (2).
{|〉 |〉} = 

√


1,0

T
,

√


1,1

T
 1
|00  |11 
√
2
2
The first concept of quantum key exchange was introduced
by Bennett and Brassard in 1984 [10]. The implementation
results in IBM laboratory of the first quantum cryptography
experiment were impressive and showed that quantum
cryptography is promising for secret key exchange [11]. The
uncertainty principle was applied in this experiment instead
mathematical modeling.
In [11], new principles were introduced for secret key
exchange against two types of intruders who intercept and
resend data. Figure 2 shows the main idea in reconciliation
between sender and receiver.
Figure 1.Rectilinear
Base
Figure 2.Diagonal
Base
978-1-4799-0048-0/13/$31.00 ©2013 IEEE
83

Figure 3. Reconciliation for Practical Quantum Key
In [12], the authors presented new security algorithm to
distribute a key over the quantum channel. In this algorithm
it is assumed that two quantum channels between the sender
and the receiver while using diagonal bases {↗, ↖} and
rectilinear bases {,}. The sender sends the same data
using two channels. The receiver measures the first
channel’s data using diagonal basis and uses rectilinear basis
for the second channel. By measuring both channels, the
receiver cancels any measured bit that has a probability less
than 1. It keeps the remaining certain bits with a probability
of 1. By this strategy the parties agree on the quantum bases
order that are used to transmit the data.
In [12], two protocols were introduced by using three party
quantum key distributions. The proposed work achieves
session agreement by using only unitary operation. In other
words, QKD is trusted from all parties, where the sender
uses some classical concepts such as checksum, and then
adds the checksum result to the original message. The main
advantage of this algorithm is that it allows authorized users
to use qubits as a session key.
A proposal introduced in [13] that supports security over
direct communications in addition to improving
authentication. The trusted server manages the
communication between authenticated users. To improve
security, the communication is divided into two stages. The
first part is called authentication and attackers check stage.
It employs hash function and unitary matrix property to
improve data authentication where each user has a unique
ID over the network. In the second stage, direct
communication occurs by dividing the data into blocks and
using entangled bits.
In [14], the authors presented a new proposal that merges
between the merits of classical cryptography and quantum
cryptography using Quantum Key Distribution Protocol
(QKDP). QKDP consists of two phases; the first step is
connection setup where the sender and the receiver agree
about the bases that can be used during the connection. The
next step is key distribution where the trusted center (TC)
notifies users about communication process. In the
beginning, TC generates a random number and a session key
by employing hashing function then sends them to the
authenticated users. When the users receive the qubits, they
measure the qubits by using the established bases from the
first phase and verify the result to check if it is the key they
agreed on or not. After the verification steps, the sender
starts sending data.
In [15], a secure algorithm introduced to improve the data
confidentiality and user authentication by using multi-party
applications. A Multicast Network Security model divides
the process into three phases. The first one is user
authentication where only legitimate users can receive
messages. In the second phase, Quantum key distribution
generates secure keys to encrypt and decrypt messages. In
the last phase, the data can be encrypted by using generated
keys from the second phase and then send to legitimate
users.
Quantum Key Distribution (QKD) protocol with a two-way
quantum channel was introduced in [16]. The algorithm
works by sending data more than once between the users
and they will compute the Quantum Bit Error Rate (QBER).
This algorithm consists of 10 steps and those steps are
repeated for 20 rounds. After the rounds, a shifted key
process is applied to agree on the bases that will be used
between the users.
In [17], Sarath et. al. proposed a scheme for digital
authentication using hash function. The scheme is utilizing
quantum characteristics and principles to perform one way
hash function. The authors proposed the scheme as an
improvement to the protocol BB84 which supports
authentication by considering programming polarizer. Dual
quantum channels are required in the scheme. The protocol
has a combination of quantum and classical processes that
provide high degree of security.
III. P
ROPOSED ALGORITHM
In this paper, we propose a three-party key distribution
protocol. Alice and Bob want to securely communicate with
each other and require a secret key to secure their
communicating channel from a trusted third party. In
protocols such as BB84 and B92, the sender and the receiver
are not able to know the secret key until the last step when
they finish the comparison of their bases. When a third party
is introduced, BB84 and B92 cannot be applied because
there is no mechanism to precisely distribute the same key
to multiple parties.
In our proposed protocol we are considering how to involve
three or more parties in the key distribution process. Our
specific aim is to improve key distribution system by
applying some classical concepts and quantum techniques.
By applying public key concepts, we can enhance user
authentication and data integrity process. The proposed
algorithm achieves a high percentage of the correct bases.
Moreover, we don’t need the physical channel to check the
Qubits sequence where the quantum bases are shared by
using asymmetric key distribution center. The proposed
algorithm consists of two phases:
1. User Authentication & Quantum Bases distribution
2. Data Transfer over the Quantum channel
In order for Alice and Bob to obtain a session key, the
following steps take place between the three parties:
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User Authentication and Quantum Bases distribution
1- Alice requests to have a connection with Bob
Alice
J
QKD: E
PR-Alice
(ID
Alice
|| ID
Bob
)
QKD will register the connection request status in log file
and check the ID of Alice for user Authentication.
Moreover, QKD checks Bob’s ID status (Busy, Free). If Bob
is free, QKD moves to step 2.
2- QKD sends to Bob a connection request containing
Alice’s request
QKD
J
Bob: E
PU-Bob
(ID
Alice
|| ID
Bob
)
3- When Bob reply by accepting the connection with Alice,
Bob will send to QKD a confirmation message
Bob
J
QKD: E
PR-Bob
(ID
Alice
|| ID
Bob
)
QKD decrypts the message and adds connection’s status
between Alice and Bob and both of them are authenticated
to send and receive data.
4- QKD starts distributing quantum bases (+,X) in some
sequence to encode the message to Alice and Bob in an
encrypted message using their public keys.
4. 1 QKD
J
Alice: E
PU-Alice
(ID
Alice
|| ID
Bob
|| QB).
4. 2 QKD
J
Bob: E
PU-Bob
(ID
Alice
|| ID
Bob
|| QB).
Data Transfer over Quantum channel
5- After Alice and Bob receive the quantum bases from
QKD, Alice sends an encrypted message using the quantum
bases to Bob
Alice
J
Bob: E
PR-Alice
(E
QB
(M)||E
PU-Bob
(ID
Alice
))
6- Bob and Alice send a random part of the message to
QKD by using Private Key of sender(Alice, Bob).
Bob QKD: E
PR-Bob
(E
QB
(M)||E
PU-QKD
(ID
Bob
))
Alice QKD: E
PR-Alice
(E
QB
(M)||E
PU-QKD
(ID
Alice
))
QKD can decrypt the messages and compare between them.
If there are any
mismatching bits, then QKD concludes
that there is an intruder.
7- QKD sends notification messages to Alice and Bob to
inform them there is an intruder or not.
QKD
J
Bob: E
PU-Bob
(E
QB
(Notify))
QKD
J
Alice: E
PU-Alice
(E
QB
(Notify))
Figure 4 and Figure 5 show the steps involved in the
algorithm.
2
. E
PU‐Bob
(ID
Alic
e
||
I
D
Bo
b
)
4
. E
PU‐Bob
(ID
Alic
e
||ID
Bob
||QB)
3. E
P
R‐
Bob
(
I
D
Ali
ce
||
ID
Bob
)
1. E
PR‐Alice
(
I
D
Alic
e
||
ID
Bob
)
4.
E
PU
‐
Alic
e
(ID
A
lic
e
|| ID
Bo
b
|| QB)
Figure 4.User Authentication and Quantum Bases distribution
If the Notify message is Okay, the connection will be alive
until QKD sends any error notification or Alice stops
sending. In the proposed protocol, we improve security
over the quantum channel. Each message is authenticated by
the sender using its private key. Moreover, data
authentication enhancement is achieved when parties send
random pieces to QKD center and notify them. By applying
this protocol we remove the guessing theory applied in early
protocols such as BB84, B92, and EPR. We have improved
the ability to identify if there is an intruder or not.
IV.
ALGORITHM ANALYSIS
Our proposed algorithm consists of two general phases and
seven steps. In this section we analyze our algorithm and
compare it with other algorithms. Table I shows a
comparison with respect to used bases, classical channel and
user Authentication. Table II, illustrates a comparison in
regards to number of used phases and the use of
cryptography.
In protocols BB84, B92 and EPR there is a probability of
mismatching bases. Taking into consideration this
possibility, the length of bases will be relatively smaller to
the original length. If there is an attacker, the percent will be
50%, which means that half of key will be discarded. In our
protocol, we can transfer the message by using the whole
key length. By using public key encryption algorithm, we
can send the quantum bases sequence from QKD to Alice
and Bob. In addition, we improve user’s authentication
where the above three algorithms do not provide it.
On the other hand, earlier protocols use classical channel to
compare between the sender and the receiver bases. In our
algorithm, the sender and the receiver send random parts
from the message to QKD to check if there is an intruder or
not.
V. C
ONCLUSION
Quantum key distribution protocols BB84, B92 and EPR
communicate using a classical channel to compare the
bases. This approach facilitates eliminating the erroneous
qubits. In this paper we introduce a novel security quantum
algorithm that employs public key encryption algorithm to
85

generate keys to improve security over quantum
communication channel. Moreover, the introduced
algorithm enhances user’s authentication and data privacy.
P
R
B
o
b
Q
B
P
U
Q
K
D
B
o
b
P
R
-
A
l
i
c
e
Q
B
P
U
-
Q
K
D
A
l
i
c
e
P
U
-
B
o
b
Q
B
P
U
-
A
l
i
c
e
Q
B
Figure 5.Data Transfer over Quantum channel
Table I. Compression between QKD, BB82, B92 and EPR
Algorithm Bases
Classical
Channel
User
Authentication
BB82 +,X Yes No
B92
Non-
orthogonal
Yes No
EPR
Entanglement
Bit
Yes No
Our Algorithm +,X No Yes
Table II. Comparison between QDKP and other protocols
Algorithm No. of phase
Classical
cryptography
[15] Two phases Hashing function
[16] Three phases XOR classical Gate
[17] One Phase Hashing function
Our Algorithm Two phases RSA
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