We propose a new system of quantum cryptography for internet security using Gaussian pulses propagating within a nonlinear ring resonator system, quantum processor and a wavelength router. To increase the channel capacity and security, the multiplexer is operated incorporating a quantum processing unit via an optical multiplexer. The transmission part can be used to generate the high capacity quantum codes within the series of micro ring resonators and an add/drop filter. The receiver part can be communicated by using the quantum key (quantum bit, qubit) via a wavelength router and quantum processors. The reference states can be recognized by using the cloning unit, which is operated by the add/drop filter, where the communication between Alice and Bob can be performed. Results obtained have shown that the correlated photons can be generated and formed the entangled photon pair, which is allowed to form the secret key between Alice and Bob. In application, the embedded system within the computer processing unit is available for quantum computer. Furthermore, such a concept is also available for internet application via hybrid communications, for instance, wire/wireless, satellite, which can be used to form the internet security.
Keywords: Internet security, Quantum computer, Quantum cryptography, Quantum signal processing
1. Introduction
The demand of using internet is increasing widely and rapidly every year. Hence, the internet security becomes an important function which is required to be included in the modern internet service. Until now, a quantum technique is recommended to provide such a requirement. However, the security technique known as quantum cryptography has been widely used and investigated in many applications [1-3]. Recently, Suchat et al [4] have reported the interesting concept of continuous variable quantum key distribution via a simultaneous optical-wireless up-down-link system. They have shown that the continuous variable quantum key could be performed via chaotic signals generated in a nonlinear micro-ring resonator system with appropriate soliton input power and micro-ring resonator parameters. They have also shown that the different time slot entangled photons can be formed randomly and can be used to select two different frequency bands for the up-down-link converters within a single system. Yupapin et al [5] have proposed a new technique for QKD (Quantum Key Distribution) that can be used to make the communication transmission security and implemented with a small device such as mobile telephone hand set. This technique uses the Kerr nonlinear type of light in the micro ring resonator to generate the superposition of the chaotic signal via a four-wave mixing type that introduces the second-harmonic pulse. A technique used for communication security via quantum chaotic has been proposed by Yupapin and Chunpang [6], where the use of quantum-chaotic encoding of light traveling in a fiber ring resonator to generate two different codes i.e. quantum bits and chaotic signal is presented. Mitatha et al [7] have proposed the design of secured packet switching used nonlinear behaviors of light in micro ring resonator which can be made for high-capacity and security switching. Such a system can also be used for the tunable band pass and band stop filters.
Both quantum communication and quantum information processing has been shown to be fundamentally different from its classical counterpart. Examples where this difference is highlighted are secure key distribution for cryptography, and the existence of fast algorithms for an idealized quantum computer. Quantum network has also been introduced and is becoming the promising technology that can be used to fulfill the perfect network security. Some research works have been reported in various forms of applications [8, 9]. The use of quantum key distribution via optical network has been reported [10, 11]. To date quantum key distribution is the only form of information that can provide the perfect communication security. The use of QKD has been proposed in many research works, whereas the applications in different forms - such as point to point link [12], optical wireless [13], satellite [14], long distance [15] and network [16] - have been reported. However, a more reliable system for network security is needed, which is both high capacity and secure. The concept of continuous variable in the form of dense wavelength multiplexing is introduced to overcome such a problem. By using the continuous variable concept, the continuous QKD can be formed and available for a large demand. Others have proposed the use of continuous variable QKD with quantum router and network [17, 18]. However, the requirement of large bandwidth signal and dense wavelength multiplexing leads to practical problems. Yupapin et al [19] have also shown that the continuous wavelength can be generated by using a soliton pulse in a micro ring resonator, and at the same time overcoming such problems.
In this paper, we have used a nonlinear micro ring resonator to form the correlated photons and quantum codes. The secret key codes are generated via the entangled photon pair, which forms the secret key for two parties known as Alice and Bob by using the Gaussian light pulse propagating with the series of micro ring resonator. In application, the device can be embedded within the computer processing unit to increase the capacity and the speed for internet, thus providing the internet security. Furthermore, such a concept is also available for hybrid communications, for instance, wire/wireless, satellite. However, the theoretical background of correlated photon source generation is reviewed.
2. Correlated Photon Generation
Light from a monochromatic light source is launched into a ring resonator with constant light field amplitude (E0) and random phase modulation, which is a combination of terms in attenuation (ï¡) and phase(ï¦0) constants. This results in temporal coherence degradation. Hence, the time dependent input light field (Ein), without the pumping term, can be expressed as
. (1)
L is the propagation distance(waveguide length).
We assume that the nonlinearity of the optical ring resonator is of the Kerr-type, i.e., the refractive index is given by
(2)
Here and are the linear and nonlinear refractive indexes, respectively. and are the optical intensity and optical power, respectively. The effective mode core area of the device is given by. For the microring and nanoring resonators, the effective mode core areas range from 0.10 to 0.50 ïm2 [20]
Fig. 1. A schematic of a Gaussian soliton generation system, where Rs: ring radii, ï«s: coupling coefficients, Rd: an add/drop ring radius, Aeffs: Effective areas, κ4.1 and κ4.2 are coupling coefficients of an add/drop filter.
When a Gaussian pulse is input and propagated within a fiber ring resonator, the resonant output is formed. Thus, the normalized output of the light field is the ratio between the output and input fields ( and) in each roundtrip, which can be expressed as [21]
(3)
Equation (3) indicates that a ring resonator in this particular case is very similar to a Fabry-Perot cavity, which has an input and output mirror with a field reflectivity, (1-ï«), and a fully reflecting mirror. ï« is the coupling coefficient, andrepresents a roundtrip loss coefficient, and are the linear and nonlinear phase shifts, is the wave propagation number in a vacuum. Here L and ï¡ are the waveguide length and linear absorption coefficient, respectively. In this work, the iterative method is introduced to obtain the results as shown in equation (3), and similarly, when the output field is connected and input into the other ring resonators.
The input optical field is described by Equation (1), i.e. a Gaussian pulse, is input into a nonlinear microring resonator. By using the appropriate parameters, the chaotic signal is obtained by using Equation (3). To retrieve the signals from the chaotic noise, we propose to use the add/drop device with the appropriate parameters. This is given in detail as followings. The optical outputs of a ring resonator add/drop filter is given by Equations (4) and (5),
(4)
and
(5)
where Et and Ed represents the optical fields of the throughput and drop ports respectively. The transmitted output can be controlled and obtained by choosing the suitable coupling ratio of the ring resonator, which is well derived and described by reference [22]. Here ï¢ = kneff represents the propagation constant, neff is the effective refractive index of the waveguide, and the circumference of the ring is L = 2°R, with R as the radius of the ring. In the following, new parameters will be used for simplification, where ï¦ = ï¢L is the phase constant. The chaotic noise cancellation can be managed by using the specific parameters of the add/drop device, which the required signals at the specific wavelength band can be filtered and retrieved. К1 and К2 are the coupling coefficients of the add/drop filters, is the wave propagation constant in a vacuum, and the waveguide (ring resonator) loss is ï¡ = 0.5 dBmm-1. The fractional coupler intensity loss is ï§ = 0.1. In the case of add/drop device, the nonlinear refractive index is neglected.
From Fig. 1, in principle, light pulse is sliced to be the discrete signal and amplified within the first ring, where more signal amplification can be obtained by using the smaller ring devices (second ring and third ring). The required signals can then be obtained via a drop port of the add/drop filter. In operation, an optical field in the form of Gaussian pulse from a laser source at the specified center wavelength is input into the system. From Fig. 2, the Gaussian pulse with center wavelength (λ0) at 1.30 µm, pulse width (Full Width at Half Maximum, FWHM) of 20 ns, peak power at 2 W is input into the system as shown in Fig. 2(a). The large bandwidth signals can be seen within the first microring device, and shown in Fig. 2(b). The signal amplification is also seen in Fig. 2(b), 2(c) and 2(d), where the amplified output of 30 W can be achieved.
Fig. 2 The Gaussian pulse with center wavelength (λ0) at 1.30 μm, pulse width of 20 ns, peak power at 2 W.
The suitable ring parameters used, for instance, are ring radii R1= 10.0 μm, R2= 10.0 μm, R3= 5.0 μm, and Rd= 155.0 μm. In order to make the system associate with the practical device [23], the selected parameters of the system are fixed to n0 = 3.34 (InGaAsP/InP), Aeff = 0.50 ïm2 and 0.25 ïm2 for a microring and add/drop ring resonator, respectively, ï¡ = 0.5 dBmm-1, ï§ = 0.1. In this investigation, the coupling coefficient (kappa, κ) of the microring resonator ranges from 0.1 to 0.70. The nonlinear refractive index of the microring used is n2=2.2 x 10-17 m2/W. In this case, the attenuation of light propagates within the system (i.e. wave guided) used is 0.5dBmm-1. After light is input into the system, the Gaussian pulse is chopped (sliced) into a smaller signal spreading over the spectrum due to the nonlinear effects[5], which is shown in Fig. 2(a). The large bandwidth signal is generated within the first ring device. By using the wider range of ring parameters, the spectral range of the output can be covered wider range instead of fraction of wavelength. The large increasing in peak power is seen when light propagates from the large to small effective core area, where the other parameter is the coupling coefficient. However, the amplified power is required to control to keep the device being realistic.
3. Quantum Key Generated by a Quantum Processor
Let us consider that the case when the photon output is input into the quantum processor unit. Generally, there are two pairs of possible polarization entangled photons forming within the ring device, which are represented by the four polarization orientation angles as [0°, 90°], [135° and 180°]. These can be formed by using the optical component called the polarization rotatable device and a polarizing beam splitter (PBS). In this concept, we assume that the polarized photon can be performed by using the proposed arrangement with each pair of the transmitted qubits randomly forming the entangled photon pairs. To begin with this concept, we introduce the technique for creating the entangled photon pair (qubits) as shown in Fig. 3. A polarization coupler that separates the basic vertical and horizontal polarization states corresponds to an optical switch between the short and the long pulses. We assume those horizontally polarized pulses have a temporal separation of ï„t. The coherence time of the consecutive pulses is larger than ï„t. Then the following state is created by Eq. (6) [24].
(6)
In the expression is the number of time slots (1 or 2), where denotes the state of polarization [horizontal or vertical ], and the subscript identifies whether the state is the signal (s) or the idler (i ) state. In Eq. (6), for simplicity, we have omitted an amplitude term that is common to all product states. We employ the same simplification in subsequent equations in this paper. This two-photon state with polarization shown by Eq. (6) is input into the orthogonal polarization-delay circuit shown schematically. The delay circuit consists of a coupler and the difference between the round-trip times of the micro ring resonator, which is equal to ï„t. The micro ring is tilted by changing the round trip of the ring and is converted into at the delay circuit output. That is the delay circuits convert into
++ +
where t and r is the amplitude transmittances to cross and bar ports in a coupler. Eq. (6) is then converted into the polarized state by the delay circuit as
(7)
By the coincidence counts in the second time slot, we can extract the fourth and fifth terms. As a result, we can obtain the following polarization entangled state as
+ (8)
We assume that the response time of the Kerr effect is much less than the cavity round-trip time. Because of the Kerr nonlinearity of the optical device, the strong pulses acquire an intensity dependent phase shift during propagation. The interference of light pulses at the coupler introduces the output beam, which is entangled. Due to the polarization states of light pulses are changed and converted while circulating in the delay circuit, where the polarization entangled photon pairs can be generated. The entangled photons of the nonlinear ring resonator are separated into the signal and idler photon probability. The polarization angle adjustment device is now applied to investigate the orientation and optical output intensity. This concept is well described by the published work [25].
The received part (RN) can be used to detect the quantum bits via the optical link. This can be obtained via the end quantum processor and the reference states can be recognized by using the cloning unit, which is operated by the add/drop filter (RdN2), used to be Bob as shown in the schematic diagram in Fig. 3.
Fig. 3. A system of the entangled photon pair manipulation of the receiver part.
The quantum state is propagating to a rotatable polarizer and then is split
by a beam splitter (PBS) flying to detector DN3 and DN4.
4. QKD via a Wavelength Router for Internet Security
The transmission part (extended from Fig. 1) can be used to generate the high capacity packet of quantum codes within the series of micro ring resonators and the cloning unit, which is operated by the add/drop filter (RdN1), used to be Alice as shown in the schematic diagram in Fig. 4. The remaining part of a system of the quantum signal and parallel processing using Gaussian pulses via an optical multiplexer is as shown in the schematic diagram in Fig. 5. In operation, the computing data can be modulated and input into the system via a wavelength router, which is encoded by the quantum secret codes. The required data can be retrieved via the drop port of the add/drop filter in the router, and the quantum secret codes can be specified between Alice and Bob. Moreover, the high capacity of data can be applied by using more wavelength carriers which can be provided by the correlated photon generation in Section 2.
Fig. 4. A system of Gaussian pulse and entangled photon generation, where RNS : ring radii ï«NS: coupling coefficients, RdNS: an add/drop ring radius, can be used as the transmission part.
Fig. 5. A system of quantum cryptography for internet security via a wavelength router, where QP: Quantum Processor, Rj : ring radii, λi : output wavelength, κj , κji are coupling coefficients.
5. Conclusion
We have proposed an interesting concept of internet security based on quantum cryptography. The system consist of two parts. The transmission part is used to generate the high capacity of quantum codes within the series of micro ring resonators. The receiver part is used to detect the quantum bits via the wavelength router and quantum processor. The reference states can be recognized by using the cloning unit [26], which is operated by the add/drop filter. A quantum processor (two add/drop filters that are in two parts) can be used to form Alice and Bob states in the link, respectively. Results obtained have shown that the multiplexed signals and quantum codes can be performed by using the wavelength router in the system, which is allowed to retrieve the secret codes by the end users (Bob). In application, the embedded system within the computer processing unit is available for quantum computer to increase the channel capacity and security. Furthermore, such a concept is also available for hybrid communications, for instance, wire/wireless, satellite.
