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A new hardware quantum-based encryption algorithm

Authors:

Abstract

Cryptography is entering a new age since the first steps that have been made towards quantum computing, which also poses a threat to the classical cryptosystem in general. In this paper, we introduce a new novel encryption technique and algorithm to improve quantum cryptography. The aim of the suggested scheme is to generate a digital signature in quantum computing. An arbitrated digital signature is introduced instead of the directed digital signature to avoid the denial of sending the message from the sender and pretending that the sender's private key was stolen or lost and the signature has been forged. The onetime pad operation that most quantum cryptography algorithms that have been proposed in the past is avoided to decrease the possibility of the channel eavesdropping. The presented algorithm in this paper uses quantum gates to do the encryption and decryption processes. In addition, new quantum gates are introduced, analyzed, and investigated in the encryption and decryption processes. The authors believe the gates that are used in the proposed algorithm improve the security for both classical and quantum computing. (Against)The proposed gates in the paper have plausible properties that position them as suitable candidates for encryption and decryption processes in quantum cryptography. To demonstrate the security features of the algorithm, it was simulated using MATLAB simulator, in particular through the Quack Quantum Library.
A New Hardware Quantum-based Encryption
Algorithm
Zakariya Qawaqneh, Khaled Elleithy, Bandar Alotaibi, Munif Alotaibi
Computer Science and Engineering Department
University of
Bridgeport
Bridgeport, CT 06604
zqawaqne@my.bridgeport.edu, elleithy@bridgeport.edu, balotaib@my.bridgeport.edu, malotaib@my.bridgeport.edu
Abstract Cryptography is entering a new age since the first
steps that have been made towards quantum computing, which
also poses a threat to the classical cryptosystem in general. In this
paper, we introduce a new novel encryption technique and
algorithm to improve quantum cryptography. The aim of the
suggested scheme is to generate a digital signature in quantum
computing. An arbitrated digital signature is introduced instead
of the directed digital signature to avoid the denial of sending the
message from the sender and pretending that the sender’s private
key was stolen or lost and the signature has been forged. The
onetime pad operation that most quantum cryptography
algorithms that have been proposed in the past is avoided to
decrease the possibility of the channel eavesdropping. The
presented algorithm in this paper uses quantum gates to do the
encryption and decryption processes. In addition, new quantum
gates are introduced, analyzed, and investigated in the
encryption and decryption processes. The authors believe the
gates that are used in the proposed algorithm improve the
security for both classical and quantum computing. (Against)The
proposed gates in the paper have plausible properties that
position them as suitable candidates for encryption and
decryption processes in quantum cryptography. To demonstrate
the security features of the algorithm, it was simulated using
MATLAB simulator, in particular through the Quack Quantum
Library.
Keywords-component;- quantum, secure communications,
qubit key, quantum cryptography, algorithms.
I. INTRODUCTION
Cryptology is the science that relies on exchanging the
indecipherable message to an unauthorized party using the
interpretation of the message not the message itself. To achieve
the ultimate goal of cryptology, an algorithm has to be used
with an appropriate key. There are classical cryptosystems that
are in use in today’s technology which are symmetric
cryptosystems and asymmetric cryptosystems. In symmetric
cryptosystems, there is only one key called secret key that is
shared between the sender and the receiver for both the
encryption and decryption, and the secret key is distributed in
most cases by third party or key distribution center.
The one time pad is classified as symmetric cryptosystem
category. One the other hand, the asymmetric cryptosystems
also called public key cryptography use two keys which are the
public key and the private key. The public key is published
publically and everyone can access it through a public
directory and the private key is kept secret and no one can
reach it.
Moreover, most complex-based encryption techniques that
provide confidentiality depend on the degree of protection
against cryptanalysis, thus a good encryption technique makes
it difficult for the attacker to know the key in a reasonable
time. However, in today’s technology, in particular the
emerging of quantum computing that can perform significant
computational operations, it is hard to defend against several
attacks such as statistical, known plaintext, and differential
attacks.
It has been discussed in literature that the security of most
classical cryptosystems is based on the assumption of
computational difficulty. Alternatively, in quantum computing,
it depends on the laws of quantum mechanics which can
guarantee unconditional security. In other words, quantum
cryptography relies and depends on physics, not mathematics.
In general, quantum cryptology can be divided to four
major areas of research which are quantum key distribution,
quantum secret sharing, quantum bit commitment and quantum
encryption which is addressed in this paper. [1]
Some quantum algorithms have been proposed in literature.
The first secure well known protocol is BB-84. The protocol
was introduced in 1984 by Bennett and Brassard. In this
protocol the message security is derived from quantum physics
fundamental laws instead of mathematical approaches. BB-84
has been implemented in several practical implementations, but
it has some technical problems, such as the use of a single-
photon sources and detectors. Consequently, this
implementation reduces the transmission distances and the data
rate. BB-84 schemes have some implementation difficulties
that are related to fiber losses which make it difficult to be
implemented in fiber optic networks [2].
The rest of the paper is divided into the following sections:
related work, proposed solution, mathematical model, results
and conclusion.
II. RELATED WORK
In 2000, Y00 protocol was proposed which deals with non-
orthogonal multi-photon quantum states. In this protocol, the
problem of decoherence has been addressed. Coherent state
could be generated and detected which could be amplified
optically and having loss tolerant. Y00 protocol is a random
cipher and has an advantage of being robust against statistical
attacks. The encoding has been implemented depending on the
light that is emitted by a laser and must be in coherent states in
which they have to be in the phase, amplitude or polarization.
In reality, quantum noise plays an integral role in preventing
eavesdropping and provides data confidentiality. Y00 protocol
was successfully implemented relying on multi-level amplitude
shift keying (ASK), polarization shift keying and phase shift
keying techniques [3].
One implementation of Y00 protocol was presented by [4]
in which a secret key is a vector k = (k1, k2, k3, … kL) that is
shared between two parties. Each symbol of a single key Kk (k
=1, 2, 3, … L) is divided into N blocks, each block consists of
m= log2 M bits which determines the base in which the sender
can map each of the sender’s message bit. The cihpertext
symbols are denoted by the non-orthogonal bases which
encode the coherent states spectrally which can be generated
using Mode Locked Laser Diode (MLLD), depending on
multiple lasing modes and pulse repetition rate which is
dividing the frequencies. The differential phase shift keying
(DPSK) and the spectral encoding modulate the message bit.
The bit can be distinguished by the key symbol denoted Kk,
multiport encoder/decoder, and phase shifters. The receiver can
easily decode the ciphertext by using the key and implementing
binary measurement.
The authors in [5] presented an improvement of ZZNXZ
scheme which was proposed by Zhou et. al. in 2006. As a
result, feasible quantum encryption algorithms were proposed
in this paper, which can entails only two key bits to encrypt
one message bit. According to the author, the resulting
ciphertext is just composed of two qubits which makes
efficient and saves about a half cost without the loss of
security, compared to (ZZNXZ), where the resulting ciphertext
for one message bit is composed of three qubits. The new
scheme is based on BB84technique.
In [1] the author presented a novel quantum block
encryption algorithm based on quantum computation. The
algorithm requires both parties (sender and receiver) to pre-
share four groups of classical keys; one will be used for
quantum ancilla bits, the other will be used for the Controlled-
NOT operation, permutation bits, and for the quantum logic
operation. The final ciphertext states are non-orthogonal.
Thus, it can mitigate any eavesdroppers.
In [6], an improved quantum cryptography protocol that
requires both of the sender and receiver to have pre-share a
secret key is proposed. The sender and receiver have to
perform “public discussion” in order to validate the session
key’s correctness. The proposed QKDPs can be a guard against
passive interception and also can do a key verification and user
authentication.
In [7], the authors proposed a new algorithm to encrypt
quantum information. In this scheme the qubits are encrypted
by hybrid keys. The hybrid keys should be shared in advanced
between the sender and the receiver. Both Hadamard gate and
Controlled-NOT gate are employed in the encryption and
decryption process. Also, the check bits process is used to
detect any eavesdropper attack. If there is no attack detected,
the same keys will be used again as same as in BB84 protocol.
The authors in [8] adapted quantum key distribution into
802.11i. The four-way handshake protocol has been amended
to supplement the BB84 protocol to the framework. In the
proposed scheme, the authors use the BB84 protocol to
establish Key Encryption Key (KEK) and the Temporal Key
(TK). The authors attach the BB84 protocol to the four-way
handshake after sending the second message. This means that
the authenticator sends the photon to the supplicant in separate
message. The quantum handshake reuses the two first
messages to enable the derivation and the freshness of the Key
Confirmation Key (KCK) before start using the BB84 protocol.
The Pseudo-Random Function (PRF) is used in the four-way
handshake by the supplication and the authenticator to derive
the Pairwise Transit Key (PTK) or the TKIP from the Pairwise
Master Key (PMK). The PTK is then divided into a KCK, a
KEK, and a TK. In the proposed scheme, the PRF only
generates the KCK which provides the mutual authentication
between the access point and the station. Two keys serving the
encryption which are the KEK and TK are constructed using
the BB84 protocol.
A scenario has been considered in [9] once Alice sends a
classical n-bit message using a classical key to Bob, and there
is only one way quantum transmission is allowed from the
sender and the receiver. In case that only short secret key is
available and the message is long, an application has been
introduced. A pseudorandom generator is used to generate
quantum cipher key streams that are derived from the short key
which is used to encrypt n-bit message block. The authors
believe that it is infeasible for the adversary to bind resources
in known plaintext attack against quantum stream ciphers.
A Secure communication scheme that provides high level
of security has been proposed in [10] to encrypt messages at
high rate. The main purpose of this scheme is to produce fast
encryption over fiber optic link. The scheme has been divided
into some layers; the Quantum Key Distribution (QKD) layer
is established on a Continues Variable Quantum Key
Distribution (CVQKD) which is introduced for secret keys
distribution over an existing fiber link. The secret key
processing contains three important components which are
error correction, physical exchange, and privacy amplification.
The commercial Thales Communication Mistral Gigabit
appliances have been integrated on the symmetric encryption
layer to develop fast session key renewal. The classical
communications is implemented on the interface layer to
generate the secret key using the raw keys that have been
introduced from the quantum link.
III. PROPOSED SOLUTION
In this paper, a new encryption technique will be
introduced as well as analyzed and investigated. The
motivation of this paper is to come up with an encryption
technique that is designated to encrypt quantum information
and send it using a classical channel as well as quantum
channel securely and efficiently.
The authors avoid depending on the one time pad operation
that has been used in most of the encryption algorithms as
discussed in the related work section. The proposed scenario is
used at the sender using the encryption algorithm. The input of
the quantum encryption would be the quantum key and the
quantum information that needs to be encrypted and sent
through the channel. Specific gates are designated in the
encryption and decryption algorithms. These gates will
enhance the security of the encryption algorithm. The proposed
algorithm considers mitigating or eliminating the possibility of
eavesdropping. The authors assume that the secret keys are
shared between the communicating parties before
communicating with each other.
In our proposed solution the authors demonstrate that it is
advantageous to use some reversible quantum gates such as
Pauli-Y gate, Fredkin gate and Hadamard gate. These gates
have many quantum properties that motivate us to see the
results of these gates in quantum cryptography.
The main goal of the proposed scheme is to produce a
digital signature in quantum computing. The digital signature is
considered to be an authentication mechanism that authorizes
the message originator to append a code that performs
signature functionality. Arbitrated digital signature is used
instead of direct digital signature because in case of using
direct signature the sender of the message can deny sending a
particular message and claims the message has been sent by
someone else and his or her private key has been stolen or lost
and the one who stole the signature has forged it. The
Acronyms and the notations that are described in Table 1 will
be used in this paper. The introduced protocol works as
follows:
a) Alice encrypts the data using |k1> and sends it to Bob.
b) Bob encrypts his new data using |k2> and sends it to the
third party.
c) Bob again concatenates his encrypted data with the data
that has been received from Alice then encrypts all the
data using the shared key |k3>. Bob sends it to Alice.
d) Alice decrypts the received data from Bob by the shared
key |k3> and splits the concatenated data. Then Alice
decrypts the data using |k1> to ensure that the data has
not been altered. Alice sends Bob’s data (which was
encrypted by |k2>) to the third party.
e) The third party decrypts the received data from Alice
and Bob using |k2> to ensure that both data are identical
and then informs both parties.
Figure1 depicts the data exchanges that occur between the
three parties.
Three reversible gates are used during the encryption and
decryption processes. These gates are Fredkin gate, Pauli-Y
gate, and Hadamard gate. After encrypting the data using one
of the mentioned keys, the encryption process in steps (a and b)
is as follow:
Apply (4*4) Pauli-Y
Apply (4*4) Hadamard (H4)
Acronyms
Meaning
|K1>
Alice’s private key (qubit)
|k2>
A pre-shared quantum key between B and
a third party
|k3>
A pre-shared quantum key between B and
A
|ѱ>
Qubit data
H
Hadmard gate
F
Fredkin gate
Tensor product operator
P
Pauli gate
R-B
Random bit to do Measurement Operation
Table 1: Acronyms and Notations
Figure 1: the proposed protocol.
The encryption of the in step (c) is as follows:
Apply Fredkin( 8*8 ) to Alice’s encrypted data
Apply Hadamard (8*8) to Alice’s encrypted data
Apply Fredkin( 8*8 ) to the Bob’s encrypted data
Apply Hadamard (8*8) to Bob’s encrypted data
Combine both data.
The sequence of the decryption process would be the
inverse of the above steps. Since the above operations are
unitary and the keys are pre-shared, it would be done easily.
As an example, the process of the encryption in steps (a and b)
is as follow:
Apply (4*4) Hadamard (H4)
Apply (4*4) Pauli-Y
Also, the following decryption processes are used in step D
which is as follow:
Split the concatenated data
Apply Hadamard (8*8)
Apply Fredkin( 8*8 )
Figure2 shows the encryption process that is done by each of
three parties.
Figure2: The encryption processes.
IV. MATHEMATICAL MODEL
Alice data |ѱ> (qubits) is encrypted with the key that has
been scaled with measurement operation. Before applying the
gates, the following algorithm in (1) is used to prepare the
tensor product,
󰇤  (1)
Where the Ki is one of the three keys (|k1>, |k2> and |k3>)
after the measurement operation and Q is the Qubit data. The
following code is used to prepare the tensor product of Alice in
step (a):
Where the Q_A is Alice’s 4 Qubits and M_op_KA is the
measurement operator for Alice’s private key.
Three gates (Pauli-Y gate, Hadamard gate, and Fredkin
gate) are used sequentially in the proposed protocol. Pauli-Y
gate is as indicated in (2):
(2)
Pauli Y gate is a reversible and unitary gate and is used
during the encryption and decryption processes.
The Hadamard matrix is represented as indicated in (3):
 
 
  (3)
The Hadmard matrix is very important in quantum
computing because it identifies the change from one basis to
another basis.
Fredkin gate has three inputs and outputs, the first input is
the control input, and the output of the first input is always the
same. If the first input is set to state 0, then the second output
would be the same as the input. The third output also would be
the same as the input. However, if the control bit set to one,
then the output would be its reverse. The overall
representation of Fredkin gate is as indicated in (4):
       (4)
V. RESULTS
Quack, which is a quantum MATLAB simulator, was used
to simulate the proposed work. Authors were able encrypt,
decrypt, match, and send the Quantum data between the three
parties. The third party was able to match the data that was
received from Bob and Alice. Three quantum gates which are
Pauli gate, Fredkin gate, and Hadamard have been used and
tested in this proposed algorithm. These gates have vital
quantum properties and can work in encryption and decryption
processes in quantum systems.
Furthermore, in comparison to Zhou et. al. protocol, the
authors have used only Toffoli gate in addition to the typical
Hadmarard gate. Fredkin gate is more complex and powerful
than Toffoli gate. Also, Fredkin gate has one more computation
level than Toffoli gate. In our proposed solution, the Toffoli
gate does not add to the complexity of the cryptography has
been replaced by Fredkin gate which can add to security of the
system because it has a swapping functionality and has better
complexity compared to Toffoli gate. Also, one more security
layer has been added which is not introduced in Zhou et. al.
protocol by passing the quantum information through Pauli-Y
gate after encrypting the data.
However the process of the communication is expected to
be slower, since the numbers of the operations that need to be
for i=1:4
Tens_QA_KA(:,i)=kron(M_op_KA(:,i),
Q_A(:,i));
End
done in the proposed scheme are more than those presented in
Zhou et. al. protocol. But, that does not affect the process of
the new proposed algorithm due to the fast hardware and the
the speedy computation process nowadays.
The authors tested several methods to disturb the
communication and alter the data in order to investigate and
measure the strength of the proposed protocol. As a result, the
entire different scenarios which have been tested showed the
strength and the robustness of the proposed algorithm against
eavesdropping. Moreover, any attempt to alter or change the
sent data was discovered immediately.
As known, in quantum computing, Eve cannot make copies
the Qubit stream and the act of measuring the Qubit would
change it. Therefore, the presence of Eve can be detected. As a
consequence, the pre-shared three keys (|k1>, |k2>, |k3>) are
reusable as long as there is no eavesdropper. If the
eavesdropper is detected, new quantum keys would be
required.
VI. CONCLUSION
In this paper, a new Quantum cryptography scheme has
been proposed to improve the quantum encryption through
both quantum and classical channel. Some of the quantum
gates have been used in this implementation. The authors
believe these gates will help improving the security in both
classical and quantum computing. Two quantum gates which
are Pauli and Fredkin gates have been analyzed and showed
that these can be used alternatively and interchangeably with
other in existence gates in quantum cryptography. The authors
demonstrated that new quantum gates can be used and be
alternative to different proposed gates in quantum realm. The
proposed gates can have excellent properties that make them
plausible candidates to quantum cryptography.
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