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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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