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Provably Secure Quantum Key Distribution by Applying Quantum Gate International Journal of Network Security, Vol.20, No.1, PP.88-94, Jan. 2018 (DOI: 10.6633/IJNS.201801.20(1).10) 88 Provably Secure Quantum Key Distribution By Applying Quantum Gate V. Padmavathi1, B. Vishnu Vardhan2, and A. V. N. Krishna3 (Corresponding author: V. Padmavathi) Associate Professor, Department of Computer Science & Engineering, Sreenidhi Institute of Science & Technology1 Hyderabad, Telangana, India Professor, Department of Computer Science & Engineering, JNTUH College of Engineering2 Karimnagar, Telangana, India Professor, Department of Computer Science & Engineering, Christ University3 Bengaluru, Karnataka, India (Email: [email protected]) (Received Nov. 26, 2016; revised and accepted Feb. 21 & Mar. 31, 2017) Abstract QKD by Wiedemann [25]. In 1984, Bennet and Brassard proposed first QKD and popularly known as BB84 pro- The need for Quantum Key Distribution (QKD) is tocol [2]. It requires two communication channels specif- strengthening due to its inalienable principles of quantum ically a classical channel and a quantum channel. The mechanics. QKD commences when sender transforms bits classical information is communicated by classical chan- into qubits or quantum states by applying photon polar- nel and qubits by quantum channel [6]. ization and sends to the receiver. The qubits are altered The two key principles of quantum mechanics are: 1) when measured in incorrect polarization and cannot be the principle of Heisenberg Uncertainty; 2) the principle of reproduced according to quantum mechanics principles. photon polarization. The Heisenberg Uncertainty princi- BB84 protocol is the primary QKD protocol announced ple states that the simultaneous measurement of physical in 1984. This paper introduces a new regime of secure properties which are related, cannot be made [2]. The QKD using Hadamard quantum gate named as PVK16 principle of photon polarization states that the qubits QKD protocol. Applying quantum gate to QKD makes cannot be replicated according to the theorem of no- tangle to the eavesdroppers to measure the qubits. For cloning [27]. Hence, the accomplishment of principles of a given length of key, it is shown that the error rate is quantum mechanics is one of the reasons why quantum negligible. Also, the authentication procedure using dig- cryptography is so powerful. ital certificates prior to QKD is being performed which In this paper, a new paradigm of quantum key distri- confers assurance that the communicating entities are le- bution scheme using one-qubit Hadamard quantum gate gitimate users. It is used as a defensive mechanism on named as PVK16 QKD protocol with authentication of man in the middle attack. two communicating entities prior to key distribution is Keywords: Authentication; Quantum Cryptography; proposed. Authentication implies secure communication. Hadamard Gate; QKD; Qubits A noteworthy characteristic of any protocol is that the information is authenticate, if authenticate entities par- ticipate in the communication. Without authentication, 1 Introduction there is always scope of an eavesdropping attack and the In 1969, Stephen Wiesner identified that quantum me- entities are fooled by impersonation. chanics has the prospective to play a vital role in the field The quantum gate applied on one-qubit can be illus- of cryptography [26]. This has become a breakthrough trated by 2 by 2 matrix [19]. Hence, the time complex- idea to recommend a new research field known as Quan- ity of quantum gates is 2n which is exponential. It is tum cryptography. It is a promising research area where proved that the exponential complexities are secure. By the secure communications happens by means of prin- embodying quantum gate into QKD protocol it becomes ciples of quantum mechanics and quantum computing. cumbersome for an eavesdropper to measure the qubits. The central unit of information in quantum computing is Besides QKD, this scheme has also adopted the process quantum bit in short known as qubit. The idea of Quan- of authentication to detect man in the middle attack. tum cryptography was put forward to project a process for Section 2 will brief about the related work in QKD and International Journal of Network Security, Vol.20, No.1, PP.88-94, Jan. 2018 (DOI: 10.6633/IJNS.201801.20(1).10) 89 authentication. The implementation of proposed protocol authentication using OpenSSL tool which provides X.509 is elucidated in section 3. Section 4 explicates the anal- authentication service. X.509 is an important yardstick ysis of results. Section 5 highlights on security analysis. to grant authentication because the pile of certificate and Section 6 presents conclusions. authentication protocols stated are used in wide range of applications. It is being formed on the use of public key cryptography and digital signatures which entail the use 2 Related Work of a hash function [12, 23, 24]. Figure 1 depicts the gen- eration of digital certificate. The last two decades has marked the evolution of Quan- tum cryptography in productive ways. With various the- oretical proposals and demonstrations using experiments, the Quantum cryptography was applied in distributing secret key. Since then, QKD has been used as a solution to the problem of key distribution. A quantum channel was developed using an optical fiber in order to imple- ment QKD in a secure fashion for over different distances like 14 kms, 24 kms [3, 7, 18]. In 2015, a highly secured network switches with QKD systems was developed [5]. In recent years, Quantum cryptography is attracting substantial attention among researchers due to major the- oretical and practical research projects related to the im- plementation of QKD. The QKD was successfully demon- strated to resist eavesdropping attacks, photon number Figure 1: Digital certificate splitting attacks, etc. using diverse protocols like Ekert's entanglement, weak coherent pulses, decoy states and op- The authentication process is carried out as shown in tical fiber [8, 13, 21, 22, 29, 30]. the following steps and described in Figure 2. The process of authentication was also carried out to ensure that the communicating entities are alleged users Step 1. Sender and Receiver requests digital certificate from past years. It was accomplished using several con- from Trusted CA before the commencement of com- cepts of quantum mechanics namely entanglement, one munication. qubit, Bell states and unitary transformations [1, 14, 28]. Also the authentication process was performed by means Step 2. CA issues digital certificates to Sender and Re- of classical XOR operation [4]. In 2009, by using quan- ceiver. tum superposition states the authentication protocol was proposed [9]. The public key authentication scheme with Step 3. Sender sends certificate to the Receiver for ver- trusted server based on discrete logarithms for cryptosys- ification. tems was also implemented [10, 11]. Step 4. Receiver sends certificate to the Sender for ver- ification. 3 Implementation Step 5. Sender verifies Receiver's certificate whether he/she is alleged user or not by using CA's public PVK16 QKD protocol is introduced to fulfill quantum key and also Receiver verifies Sender's certificate. key distribution using Hadamard gate. It is implemented using MatLab R2014a [15]. The authentication procedure is carried out through digital certificate using OpenSSL 3.2 PVK16 QKD Protocol - Quantum tool [20] to detect man in the middle attack. Key Distribution Using Hadamard Gate 3.1 Authentication Hadamard gate is a one-qubit quantum gate.p It takes Authentication avoids Sender and Receiver being fooled either qubitp j0i or j1i as input and gives 1= 2(j0i + from illicit user. In order to provide authentication, we j1i) or 1= 2(j0i − j1i) as output respectively [2]. use the notion of digital certificate. It embodies the The Hadamard gate is denoted as | H |. hashed user's public key which is encrypted with the pri- The matrix representation of quantum gates is derived vate key of a trusted certification authority (CA) to form using tensor product. The tensor product combines two digital signature. The CA issues certificate to the commu- vector spaces to form a larger one. If U and V are vector nicating entities upon request. They verify each other's spaces of dimensions m and n respectively then U ⊗ V is certificate by decrypting signature with CA's public key. a space on mn. The elements of U ⊗ V are linear combi- With this they will get assurance that each other is com- nations of tensor products ju > ⊗|v > of elements of ju > municating with legitimate user. We have implemented of U and jv > of V . Suppose A is a m by m matrix and International Journal of Network Security, Vol.20, No.1, PP.88-94, Jan. 2018 (DOI: 10.6633/IJNS.201801.20(1).10) 90 Figure 2: The process of issuing and verifying digital certificate B is a p by q matrix, then the matrix representation is • b(f0; 1gn): Sender's bit string, n is the original given as length of the secret key. 2 3 • d(f0; 1gm)jm ≤ n: Receiver's bit string. A11BA12B:::A1nB n 6 A21BA22B:::A2nB 7 • θa(f+;Xg ): Sender's bases in string. A ⊗ B = 6 . 7 6 . 7 m 4 . 5 • θb(f+;Xg )jm ≤ n: Receiver's bases in string. Am1BAm2B:::AmnB m • Rf0; 1; θbg jm ≤ n: Receiver's measurement Hence, to represent Hadamard gate which is one-qubit string. gate, a 2 by 2 matrix is needed as shown below [2, 17]. • U: Undetected positions. p 1 1 H = 1= 2 1 −1 p j0i ! H = 1= 2(j0i + j1i) p j1i ! H = 1= 2(j0i − j1i) Figure 4: Rectilinear and diagonal bases The procedure of new protocol of QKD using Hadamard gate namely PVK16 QKD protocol is depicted in Figure 3. Step 1. Sender's preparation of qubits. Sender selects random bits 'b' in sequence manner where b 2 (f0; 1gn), n is the original length of the secret key. Then he/she prepares qubits for those bits individually in one of the four states of BB84 protocol using rectilinear '+' and diagonal 'X' bases shown in Figure 4.
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