Optical Chaos KEY generator for Cryptosystems

Chaotic structures are ideally appropriate for the construction of cryptographic schemes, because random numbers are an inseparable part of every encryption scheme as a safety mechanism. The optical chaotic circuit is an ultra-fast physical Random number generator, which is illustrated using the CW laser that generates optical signal at 193.1 THz and M-Z modulator that works on an interferometric principle. The circuit generates truly high random bit sequences at different higher bit rates of 320Gb/s and 640 Gb/s. These generated random bits have passed the NIST statistical tests and Diehard battery tests, indicating their randomness for different practical applications. Further, the random number generated by optical chaos circuit is used to secure the image data using RC4 ciphering method.


Introduction
In the present era, data security is playing the significant role in the field of Information technology and computer network communications. The cryptography is one such essential system to provide ultimate security for the information. To achieve this, random numbers are one of the important components to store the data securely in storage devices either by using encryption or hiding techniques. Therefore, there is a requirement for generating high quality random numbers at a higher bit rate. Such random numbers should have a uniform distribution of data across their range and there should be no way of estimating past or next value, i.e. unpredictability. The recent developments in research shows different approaches to strengthen the security. The main approach is the optical chaos circuit for generating complex chaotic analog signals for the implementation of secure communication systems. They also provide the seed required for generating fast and high quality physical random numbers for various cryptographic applications.
The research in quantum based TRNG s demonstrated different methods that could increase the bit rate efficiently and potentially over 100Mb/s. However, the recently proposed techniques demonstrate that the bit rates are significantly slower than the bit rates that can be obtained by using chaotic signals generated by semiconductor lasers. Semiconductor lasers results unstable operating behaviour even for very small external reflections and perturbations as they are very sensitive to external optical light. So, all types of commercial semiconductor lasers can be applied to the standard network communication systems. These lasers with feedback are very interesting subject in terms of nonlinear dynamic behaviour they exhibit and their potential for different applications [1,2]. A semiconductor laser with a delayed optoelectronic feedback loop is also an effective broadband chaos generation technique that uses a combination of a photodetector and an amplifier to transform the optical output of the laser to an electrical signal that must be fed back to the laser via electrical feedback [3]. A 1.7Gb/s TRNG was implemented using binary digitization of two independent chaotic semiconductor lasers to achieve efficient and stable generation of random sequences at higher frequencies. A logical XOR operation was used to combine binary bit signals obtained from the two independent lasers. A single chaotic source could not be adopted as they would cause bias in the final result due to periodicities of the external cavity modes of each chaotic waveform [4]. To increase the speed still further, multimode semiconductor laser was implemented to achieve the bit rate up to 12.5Gb/s. This multimode method operates in the coherence collapse regime due to feedback from the external source [5,6,7]. Finally, Compact photonic integrated circuits were used to exploit broadband signals to generate random bit sequence at a bit rate of 140Gb/s. This uses PIC and MSB elimination post processing method to generate real time bit sequences from an oscilloscope's ethernet output port [8,9,10].
This paper presents ultra-fast physical optical chaos RNG, which is demonstrated using the CW laser that generates optical signal at 193.1 THz and MZ modulator which works on an interferometric principle. This method generates the binary sequences at different bit rates of 80Gb/s,160Gb/s and 640Gb/s. The rest of the paper is organized as follows: In Section-2 block diagram of the proposed method and working operation of each sub blocks are discussed, Section-3 includes the simulation results of the circuit diagram and randomness test results conducted using NIST and Diehard battery test. In section-4 RC4 Stream cipher algorithm and encryption and decryption results are discussed. Section-5 concludes the overall work. Figure 1 shows the general block diagram of the optical chaos random sequence generator. It mainly consists of (i) Optical chaos signal generator which uses user defined initial value and optical source to generate chaos signal, (ii) Optical to electrical signal converter, (iii) Analog electrical signal to digital electrical signal converter and (iv) Extraction of binary sequence.  Figure 2 shows the Block diagram of Optical chaos signal generator in which the output chaos signal depends on the user defined initial value. Single bit changes in the initial predefined user value results with greater change in the resulted chaotic signal. The CW Laser is used as an optical source to generate continuous optical signal at a frequency of 193.1THz. In CW Laser, the average output power is a parameter that user can specify. The laser phase noise is modelled using the probability density function shown in equation (1):

Proposed method
Where Δφ is the phase difference between two successive time instants and dt is the time discretization. A random Gaussian vector for the phase difference between two consecutive time instants with zero mean and a deviation equal to √ has been assumed, with Δf being the laser line-width.
The polarization controller sets the CW signal to the arbitrary polarization state, in which appropriate component will be selected and split into two parts using polarization splitter. The operation of polarization splitter is indicated in figure 3. The modulator Mach-Zehnder is used to modulate the one component of the optical split signal, which utilizes electrical voltage by causing opto-electric influence. The initial value specified by the user is used to produce the electrical voltage. It is essentially an intensity modulator that operates on an interferometric principle (i.e., the superposition principle for mixing waves to evaluate the initial wave state). It consists of two 3 dB couplers, which are connected by two similarly long waveguides (Figure 4). An externally applied voltage can be used by way of an electro-optic effect to adjust the refractive indices in the waveguide divisions. Based on the voltage applied, the numerous paths may create positive and destructive interference at the source. Then the output intensity can be modulated according to the voltage which is given by equation (2) . E out (t)=E in (t). cos (Δθ(t)). Exp (j.Δ ( t ) Where, Δθ is the phase difference between the two branches and Δϕ is change in the signal phase.  The modulated wave will be combined with another part of the original signal using polarization combiner to generate the optical chaos signal. The generated chaos signal will be passed to the optical to electrical signal converter for further processing through single mode optical fiber.

Optical signal to Electrical signal converter.
The received signal can be used to monitor the transmission error and to improve the output strength (i.e. to enhance the signal) by means of the optical fiber ideal Isolator and the Erbium doped fiber amplifier. Figure 5 shows the block diagram of the Random bit sequence generator. To control the insertion loss and to improve the output power (i.e.to strengthen the signal) of the transmitted signal through optical fiber ideal Isolator and Erbium doped fiber amplifier will be used. EDFA is used mainly in C-band and L-band for long distance optical communication whose wavelength ranges from 1530 nm to 1565 nm and 1565 nm to 1625 nm respectively. Finally, APD (Avalanche photodiode) component is used to convert optical signal to electrical analog signal.

Post processing.
The electrical analog signal should be processed to obtain the binary sequence. The Analog-to-digital converter (ADC) converts analog signals into a digital format which consists of two-step process: sampling at the ADC sample rate and quantization according to the resolution. These multilevel pulses are translated to the M-ary signal output using the threshold detector and the binary sequence is retrieved using the QAM (Quadrature Amplitude Modulation) sequence decoder. Based on bits used to represent the sequence it is possible to generate different bit rate data. QAM of 2,4,8,16 and 32bit, is generating the binary sequences at a bit rate of 20Gb/s,40Gb/s,80Gb/s,160Gb/s and 320Gb/s respectively.

Simulation results
OptiSystem is a software package for optical communication device that enables the user to design, test and simulate optical links in the transmission layer of advanced optical networks. In this paper, circuit has been designed and simulated using the OptiSystem 16 software. Figure 6 shows the simulated circuit diagram of the proposed method, in which built-in components are used with proper specifications. Figure 7 displays the random signal produced by the optical chaos circuit, demonstrating that the signal is random in nature. The random signals are converted to binary bits by carrying the signal through the M-ary phase detector and the QAM decoder.   Figure 8a and 8b indicate that all statistical tests are passed implying that the generated binary bit sequence is random in nature.

B. Security key analysis
The length of the user key is 65,536 bits with the key space of uncountable. It is so large enough to defend against the brute-force attack. Further, this key space can be expanded to satisfy the future requirement based on different applications. Table 1 shows that a number of bits differ in the output binary sequence even for a small bit difference in the initial user defined value demonstrating the avalanche effect in random sequence.

C. Security data analysis
In order to provide data protection, it must be encrypted before it is transmitted via the transmission medium and decrypted on the receiver side. So, the implementation of the RC4 stream cipher system provides data protection, as it uses extremely random bits as the key value to perform encryption and decryption.

RC4 stream cipher
The RC4 is a simple and fast stream symmetric cipher algorithm that do not require more memory. It is easy to implement and works on the basis of single byte manipulation to construct long keystream sequences. Encrypts data by executing XOR operation byte by byte, serially using keystream bytes. The entire RC4 algorithm is based on the development of keystream bytes. There is no need of any LFSR (Linear feedback shift registers) registers. It consists mainly of two parts: the initialization of the key stream and the generation of the key stream. Figure 9 displays the RC4 stream cypher block diagram.

Encryption and Decryption results
The image shown in figure10a is encrypted and decrypted using the RC4 Stream cipher method which uses the key stream generated by an Optical chaos circuit. Figure 10b and 10c shows the encrypted and decrypted images respectively.

Conclusion
In this work, semiconductor lasers are used as a chaotic source since they are extremely responsive to external optical light. Unstable operating behaviour of laser able to produce broadband optical chaotic signals that have been used to for generating KEYs at high bitrate of 160-640Gb/s. Tests on these KEYs have shown that they are strongly random in nature. The RC4 stream cypher that uses optical chaos keys to encrypt images is found to have high security. As a result, we infer that the optical chaos KEY generator is one of the promising technique that can be used for data security.