Development of authentication code for multi-access optical code division multiplexing based quantum key distribution

Optics and Laser Technology 101 (2018) 312–318

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Development of authentication code for multi-access optical code division multiplexing based quantum key distribution Ambali Taiwo a,⇑, Ghusoon Alnassar a, M.H. Abu Bakar a, M.F. Abdul Khir b, Mohd Adzir Mahdi a, M. Mokhtar a a b

Computer and Communication Sys. Engineering/Center of Excellence for Wireless and Photonic Network (WiPNET), Faculty of Engineering, University Putra Malaysia, Malaysia Information Security and Assurance Programme, Faculty of Science and Technology, Universiti Sains Islam Malaysia, Bandar Baru Nilai 71800 Nilai, Negeri Sembilan, Malaysia

a r t i c l e

i n f o

Article history: Received 11 January 2017 Received in revised form 4 October 2017 Accepted 20 November 2017

Keywords: Authentications Key distribution Information security Quantum communication Cryptography

a b s t r a c t One-weight authentication code for multi-user quantum key distribution (QKD) is proposed. The code is developed for Optical Code Division Multiplexing (OCDMA) based QKD network. A unique address assigned to individual user, coupled with degrading probability of predicting the source of the qubit transmitted in the channel offer excellent secure mechanism against any form of channel attack on OCDMA based QKD network. Flexibility in design as well as ease of modifying the number of users are equally exceptional quality presented by the code in contrast to Optical Orthogonal Code (OOC) earlier implemented for the same purpose. The code was successfully applied to eight simultaneous users at effective key rate of 32 bps over 27 km transmission distance. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction Ever since its discovery three decades ago [1], quantum cryptography has maintained its exceptionality in providing anticipated secure mechanism between two communicating ends. Its security establishment has remained a promising solution to the challenges posed by the progress towards quantum computing, a rare opportunity that might be explored to mount attack on the existing security system that relied on mathematical complexity. Quantum cryptography often referred to as quantum key distribution (QKD) proffers its security measure by exchange of set of random bits between two users [2–4], which upon series of post-processing, are used in the generation of secured key for information exchange. Its security provision, guaranteed by fundamental law of physics [2,4–6] has remained unconditional in the presence of eavesdroppers. Over the years, tremendous progress have been recorded in the area of the security enhancement against all emerging loopholes in various QKD protocols [4, 7–9] One of the most appealing among them is the decoy state system [2], which provides security against Photon Number Splitting (PNS) attack. This has been achieved through additional pulses that tends to raise an alarm whenever alteration is perceived in the intensity of the received pulses. This ⇑ Corresponding author. E-mail address: [email protected] (A. Taiwo). https://doi.org/10.1016/j.optlastec.2017.11.034 0030-3992/Ó 2017 Elsevier Ltd. All rights reserved.

eventually lessens the impending challenges in practical QKD that are based on weak pulse laser source. Subsequent works focused on the transmission distance and secured key rate. The first practical implementation of QKD was only achieved over 30 cm distance. The latest development have reported between tens and hundreds of kilometers [10,11 which have been achieved both theoretically and in practical. A number of works on the other hand, focus on improving the secret key rate while sacrificing the supported transmissions distance. A key rate of 1 Mb/s was recently reported in [12] over a distance of 20 km and 50 km [13] respectively. One specific thing about all the above-described works is that they are only addressing a pointto-point communication between two end users. The latest trends in QKD development are unequivocally exploring the multi-user ability of the system. Imagine an establishment with several sections within a certain location. Each user requires a distinctive way of identification with minimal resources. Subcarrier QKD multiplexing was proposed in [14] and further developed in [15,16]. The technique, which saw bands of diverse frequency used in modulating the weak pulse laser, was subsequently experimented for two users in [17]. Its low key rate was due to complexity in the system design. Subsequent work include Orthogonal Frequency Division Multiplexing of QKD (OFDM-QKD) [18] proposed in 2015. The system recorded better performance only with activate decoding technique which subsequently add to the cost and complexity of the design. Previously in 2012, Razavi

A. Taiwo et al. / Optics and Laser Technology 101 (2018) 312–318

proposed a thrilling multi-access QKD system based on OCDMA system [19]. The system was demonstrated with both passive and active decoders. The active system is a form of ‘‘listen-befor e-send” approach whereby both communicating ends pay attention to the channel to ensure it is unengaged before transmission. The work however made use of Optical Orthogonal Code (OOC), which has complexity in its derivation as well as longer code length, with heavy spectral dependency on the light source [20, 21]. This work proposed a new code, which is suitable for multiplexed QKD system. As established in [19] that a single weight code has proximity in performance to time division based system than multi-weight code, the proposed code is also a singleweight code which at the same time, is secured against channel attack. One other unique characteristics of the code is that it could equally be used as time-dependent code with all users sharing the same frequency spectrum at distinctive time interval. The paper is organized as follows; Section 1 contains the introductory part while Section 2 vividly describes the proposed code derivation. The system setup will be addressed in Sections 3 and 4 will explain the mathematical derivation of the system. The results will be discussed in section 5 and the concluding part will be addressed in Section 6.

313

The patterns are then treated as sets of binary digit and subsequently converted to their respective decimal equivalents by adding their corresponding decimal values horizontally.

The obtained decimal values {x = 384, 192, 48, 24, 6, and 3} are divided by the common factor ‘‘3” to form the new pattern {128, 64, 16, 8, 2, 1}. These are subsequently converted to their respective binary form to generate the usable code sequence.

2. Proposed code design The code begins with the formation of a matrix with a logical pattern of binary digit ‘‘1” and ‘‘0” denoting presence and absence of a certain pulse. The bits are arranged in 3
2 matrix with the first two bits position of the first row and last two bits position of the second row occupied by bit ‘‘1” as shown in the matrix.




1 1 0 0



1 1

The bit pattern can then be increased by diagonal repetition of the matrices.

2


1 1 0 6 0 1 1 6 6 6 6 6 6 6 4

3






1 1 0



0 1 1

7 7 7 7 7 7 7
7 1 1 0 5 0 1 1

The patterns are combined in a large matrix to form a single matrix with N column and M row. This ensures that the element are located along the major diagonal in the matrix.

2

3

1 1 0

60 1 1 6 6 6 6 6 6 6 4

1 1 0 0 1 1

7 7 7 7 7 7 7 7 1 1 05 0

1 1

The emerging vacuum are subsequently filled with bit ‘‘0” to obtain a full pattern of binary sequence.

2 6 6 6 6 6 6 6 6 4

0

3

1 1 0

0

0 0

0

0

0 1 1

0

0 0

0

0

0

0

0

1 1 0

0

0

0

0 1 1

0

0

0

0

0 0

07 7 7 0 0 07 7 0 0 07 7 7 1 1 05

0

0

0

0

0 0

0

1 1

With each row as a unique address location, each user can uniquely communicate with their respective partners on the channel with no or minimal interference from the adjacent users. The chip locations are diverse wavelength corresponding to the column value as shown in the final derivation above. One other unique characteristic of the proposed code is occasional presence of ‘‘all zero” column. Unlike the conventional channel code for classical OCDMA system where overlapping of chips are used to determine the level of security, the level of ambiguity in predicting the exact spectrum being used by a certain users in the derived quantum code could as well serve as a source of security. Other benefits of the code is flexibility in modifying the required number of users to suit ones purpose. Theoretically, the number of users can further be increased through the formation of matrix C i;j with the position of the bits corresponding to

2

C 0;0 6. 6 .. C i;j ¼ 6 6 4 C m;0

3 C 0;n 7 .. 7 . 7 7    C m;n 5

 .. .

For i ¼ 0; 1; 2; . . . . . . . . . :m and j ¼ 0; 1; 2; . . . . . . n. The positions of ‘‘1” in Table 1 are at row (i) and column (j) locations described as

C 0;1 ¼ C 1;2 ¼ C 2;4 ¼ C 3;5 ¼ C 4;7 ¼ C 5;8 ¼ 1 In order to derive the location mathematically, the following steps are followed. Step 1: Count j from 0 and increase by 1 in each stage. j = 0, 1, 2, 3, 4 . . . Step 2: To find column with all ‘‘0”. All element of a column will be ‘‘0” if jmod3 ¼ 0.

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Table 1 Proposed code pattern for six users. k1

k2

k3

k4

k5

k6

k7

k8

k9

0 0 0 0 0 0

1 0 0 0 0 0

0 1 0 0 0 0

0 0 0 0 0 0

0 0 1 0 0 0

0 0 0 1 0 0

0 0 0 0 0 0

0 0 0 0 1 0

0 0 0 0 0 1

Step 3: For column with ‘‘1” value, a variable k is introduced,  where k =  j  (ceiling division round down). The corresponding 3

value of i for j so that C i;j ¼ 1, is i ¼ j  k  1. 3. System setup The proposed code is validated in simulation with the setup depicting the commercial available (IDQ Clavis 3000) plug and play QKD system. The system is chosen as it does not require path control between sender (Alice) and receiver (Bob), no bi-fringence effect and more so, has been commercialized in pluggable modules. Each unit consisting of a Gaussian pulse laser is emitting pulses at frequency of 5 MHz. For the sake of illustration and simplicity, eight laser pulses, which are spaced at 600 ns interval, were used in our Optisystem simulation demonstration. The pulses propagate through a circulator into a two-arm interferometric setup comprising a short arm and a long arm. The longer arm consist of a phase modulator and a delay line that introduced a time delay of 300 ns. Both pulses (P1 and P2 from short and long arms respectively) are then coupled through a polarization maintaining coupler, which rotate P2 from the longer arm by 90° so that the two pulses will exit the coupler through the same port. The outputs pulses are then encoded using Fiber Braggs Gratings (FBG) based on the proposed code pattern. The wavelengths are maintained at 1 nm spectral width to each other with the first chip of 1552.0 nm. The encoded pulses are then coupled with other adjacent transmitters as depicted in Fig. 1 and propagated through the quantum channel. At the receivers’ side, the signals are divided into the number of receivers and subsequently decoded with the corresponding decoders. Each receiver Alice(i) with i ¼ 1; 2; 3; . . . . . . n; comprises of an attenuator, which attenuate the signal to the required mean photon (m) of 0.48 and a phase   modulator which randomly modulate the pulses into 0; p; p2 ; 3 p2 . Also at Alice is a delay line, which temporarily holds the transmitted train of pulse until return of the previous one, and a Faraday mirror that rotate and reflect the qubit stated in orthogonal form.

Meanwhile only P2, which was previously delayed at Bob will be modulated by Alice phase modulator while the first pulse P1 will pass freely and be rotated by Faraday mirror. The pulses upon returning to the Polarization maintaining coupler took different path with P2 taking the shot arm while P1 takes the longer arm in contrast to when they were first launched. At this time, P1 will be delayed by the same time 300 ns and modulated randomly at   Bob with either of 0; p2 . Having passed through the same optical length, both pulses arrived at coupler 1 simultanously, leading to generation of either a constructive or destructive interference. It becomes constructive if both Alice and Bob apply the same phase rotation £A  £B ¼ 0 and detructive if otherwise £A  £B ¼ p. If the inteference is constructive, the signal is forwarded toward the light source and collected on detector D1 through the circulator. A destructive one is received through detector D2. This was undoubtedly proven in our simulation as shown in Fig. 2(a)–(d) with (a) and (b) representing the received spectra at D1 and D2 when Alice and Bob applied identical phase information which generateed a phase difference of ‘‘0”. Fig. 2(c) and (d) are the received pulses when they both applied different phase information amounting to £A  £B ¼ p. It can be seen clearly that the original pulses are recovered at receiver D1 and D2 when the phase differences are 0 and p respectively. This shows that our system design is a replica of the existing plug and play QKD system.

4. Numerical derivations The mathematical derivation is in accordance with [22] with the raw key rate of each user; ðiÞ Rraw ¼ qmlt AB t B gB gduty gs =N

ð1Þ

where q is 0.5, which denote the probability of compatibility between Alice and Bob in BB84 protocol used. v is the pulse rate

Fig. 1. Schematic diagram of the system setup.

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315

Fig. 2. Received spectrum at (a) D1 and (b) D2 when both Alice and Bob applied the same phase information, leading to generation of phase difference of zero. Received at (c) D1 and (d) D2 when they both applied different phase rotation, leading to Pie.

aLþbþd

which is 5 MHz, t AB ¼ 10 10 =N is the transmittance of the quantum channel, tB is Bob transmittance, gB is Bob detection efficiency, gduty is the reduction factor introduced by delay line to the key rate. It is a ratio of delay line to the sum of delay line and transmission line [22].

gduty ¼

LD LD þ LAB

ð2Þ

gs is the alteration to the raw key rate introduced when the dead time is modified to the value 4 ms, with intent to reduce afterpulse effect [22]

gs ¼

1 1 þ v pdet s

ð3Þ

where pdet is the detection probability, s is the detector dead time, N is the number of users, L is the length of the quantum channel, b is the insertion loss of the FBG used and d is the coupling loss. The quantum bit error rate is calculated as follow [22,23]

QBER ¼ QBERoptial þ QBERafterpulse þ QBERdarkcount þ QBERstraylight

ð4Þ

where QBERoptical is the probability of the photon being received at the wrong detectors. This does not vary with fiber length and can simply be measured by calculating the ratio of the detection at both detector when a strong pulse is applied [23].

QBERoptical ¼

1V 2

V ¼ v isibility: ¼

Highv alue  Lowv alue Highv alue þ Lowv alue

ð5Þ ð6Þ

Both QBERafterpulse , which is the error due to after-pulse detection and QBERdarkcount , which is the error due to dark count, vary with the condition of the photodetector used [22,24]. QBERdarkcount in the other hand is expressed as

QBERdarkcount ffi

pdark t AB t B gB l

ð7Þ

QBERafterpulse results to gs earlier calculated. QBERstraylight is the error introduced by back scattered light in the system. This has been suppressed with the help of Alice delay line. The consequence of the delay line is the gduty which reduces the overall key rate in the proportion estimated at Eq. (2). During error correction and privacy amplification, the final key rate is further reduced by a factor gdiff , which is the difference between the amount of Alice to Bob information and Alice to Eve Information [22].

gdiff ¼ InAB  InAE Alice to Bob information InAB however is [23]

ð8Þ

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A. Taiwo et al. / Optics and Laser Technology 101 (2018) 312–318

InAB ¼ 1 þ Dlog2 D þ ð1  DÞlog2 ð1  DÞ

ð9Þ

where D is the disturbance corresponding to the total QBER. For a system where the QBER is within the estimation at Eq. (2), following the assumption in [22], an approximate QBERoptic of 0.5% is estimated for Eve with another 0.5% for estimation error, totaling 1% error. If Eve is in possession of a perfect detector, this corresponds to 3% [25]. In order to estimate the amount of information leaked to Eve due to multiphoton from the source, the optimal maximum amount is calculated based on [26]

IðA; EÞ ¼ c

l 2

að1  aÞ þ ð1  cÞ

1 2

ð10Þ

where c and a respectively are the yield of the Bob detection, and the fraction of pulses tapped by Eve by using optical coupler. With maximum a probability of ½ and the minimum Bob yield c of 0, the optimal amount of Alice information will be 0.5 at average photon number of 0.48 used in our estimation. This calculation is based on possibility of Eve using fiber with low loss of 0.15 dB/km. The total information accessible to Eve on each user is then [22]

InAE ffi 0:03 þ IðA; EÞ

ð11Þ

The overall key rate therefore becomes

Rsecret ¼ gdiff ðRðiÞ raw Þ

ð12Þ

5. Result and discussions One other specific advantage of the multiplexed system used in this work in contrast to the tree configuration with switch in [27] is inability of the eavesdroppers to distinguish the photons. As shown in Fig. 3, Eves has low chance of predicating the source of the intercepted pulse. With one user, the pulses will be known with 100% probability. However, as the number of users becomes two, Eve has only 50% probability of predicting the rightful owner of the attacked pulse. By further increasing the number of users, her chances further decreases, and if the number of users is extended to 10, she only has 10% probability of predicating the right pulses. With reduction in the probability of predicting the source of the pulses and security of the code’s architecture, high photon number ðlÞ, which is capable of supporting multi-users system can be adopted without jeopardizing the secrecy of the system. In view of this, Fig. 4 shows the various graph of the logarithm of the secrete key rate against (a) the supported distance and (b) the supported number of users at different mean photon number from 0.1 to 0.5. The graphs show increment in the supported transmission distance as the mean photon is increased.

Fig. 3. Graph showing the probability of Eve prediciting the right pulses from the wrong ones.

Fig. 4. (a) Log of secrete key rate against transmission distance (b) secrete key arte against the number of supported users.

It then slopes down regressively due to fiber attenuation and at a point, drops down to the minimum value as a result of Eves maximum attack power, a behavior similar to what was obtained in [26,28]. Base on the aforementioned and as used in some other related work [19,18], mean photon number ðlÞ of 0.48 is used all through in our subsequent analysis. As depicted in Fig. 5(a), showing both the raw key rate and the secure key rate against the supported transmission distance, a key generation rate 4.2 Kbps was achieved over a transmission distance of 5 km for two simultaneous users. As the distance increases, both key rates decay exponentially to 11 bps and 0.6 bps at 95 km. A corresponding change is observed when the number of users is increased from 2 to 10 users. The rapid fall in the key rate is due to splitting loss across the fiber splitter, which was set based on the existing splitter parameter as shown on Table 2. Fig. 5 (b) depicts the logarithm of the secret key rate against the supported distance. The graph clearly shows the maximum supported distance amidst the loss due to error correction and privacy amplification process. By increasing the number of users to 10, an approximate transmission distance of 13 km could still be achieved. Fig. 5(c) show the corresponding QBER against the distance for the observed number of users while the amount of loss dues to error correction and privacy amplifications are equally indicated in Fig. 5(c). In subsequent analysis, the impact of changing the pulse rate on the final secret key was investigated. The frequency range which were sampled at 1 MHz interval from 4 MHz to 10 MHz were

A. Taiwo et al. / Optics and Laser Technology 101 (2018) 312–318

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Fig. 5. Analysis of the performance of the proposed code base on (a) the raw key and secret key against the supported transmission distance (b) log of secrete key rate against the supported distance (c) QBER against the distance (d) the amount of key lost due to error correction and privacy amplification.

Table 2 Components parameter table. Parameters

Values

Average number of photons per pulse Detection efficiency Laser pulse repetition rate Storage line Bob transmittance Fiber attenuation FBG insertion loss Dead time Dark count probability Visibility Splitter 1
2 Splitter 1
4 Splitter 1
8 Splitter 1
12 Delay time at long arm in simulation

0.2–0.48 0.1 5 MHz 12 km 0.6 0.25 dB/km 0.2 dB 0.4 ns 105 0.98 [22] 3.2 dB 6.4 dB 10.2 dB 15 dB 300 ns Fig. 6. Key response to variation in the laser pulse rate.

tested to observe their impacts on the achieved final key rate. The assessment was done over different number of users ranging from 2 to 8 tested over 5 km distance. A matching increase in the final key rate is observed as the frequency increases. Higher rate was however achieved with less number of simulatenous users. By further increasing the number of users, the generated key rate becomes trifling as may not be considered useful for secure communication (see Fig. 6). This can be related lucidly that the maximum number of users that can be supported, using an average photon number of 0.48 is undoutably 8 within the specified frequency range.

6. Conclusion We have proposed and effectively applied a new authentication code for multi-user quantum key distributions system. The oneweight code, which is uniquely assigned to individual users on the channel created a state of ambiguity for the attacker in identifying the authentic sender of the pulses. The code was tested and proved robust in addressing the emerging channel attack challenges that are confronting the weak laser based QKD network.

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