200 Mbps real-time true random bit generator based on polarization noise in a VCSEL

Abstract

We report a prototype of real-time physical true random bit generator based on a polarization noise in a verticalcavity surface-emitting laser (VCSEL) with a bit rate more than 200 Mbps. A comprehensive statistical analysis of bits sequences performed by means of three standard tests of randomness (ENT, Diehard and NIST) shows a high quality of generated random bit sequences. Keywords— VCSEL; polarization noise; true random bit generation; prototype Random numbers play an important role in different fields as quantum and classical cryptography, programming, MonteCarlo simulation. Development of such devices possessing a high rate of the bit generation, compactness, a low cost and a high quality of output random bits sequences is an important task and attracts much attention. Here, we present a prototype of fast real-time physical true random bit generator with the rate of more than 200 Mbps. Recently [1], it was shown in offline experiments that fluctuations of a polarization-resolved intensity in a VCSEL can be used as an effective source of randomness for the fast random bits generation. Such a stochastic polarization dynamics in VCSEL is induced by spontaneous emission noise. For a large enough value of the injection current, polarization noise in a VCSEL becomes very high and occurs at a sub-nanosecond time-scale. One can find specific conditions wherein a distribution of the fluctuations is close to a normal distribution. Such a regime of a polarization noise is used in our generator. The prototype of the physical random bit generator includes two main parts: the laser module with electric circuits of temperature and the injection current stabilization, and the digital part used for data processing. The laser module consists of a VCSEL, polarizer and Si-photodiode with a rise time of 10 ns. All components were mounted in a DIL14 package. The laser intensity on the selected polarization is converted and amplified into an electrical stochastic signal, and digitized using an analog-to-digital converter (ADC) with the sampling frequency of 65 MHz and the amplitude resolution of 14 bits. In such experimental conditions the min-entropy evaluated from our experimental data was about 10 bits. It was shown recently [2] that the symmetry of a distribution of stochastic data is a necessary condition for the generation of the unbiased bit sequences. Therefore in our prototype we have used a symmetrization of the experimental date based on the application of the high-order finite difference procedure developed in [2]. Such an operation allows one to obtain a highly symmetrical distribution and reduces the dependence on the variations of the experimenal conditions. In our prototype we use the finite difference of the 40th order resulting in a decrease of the coefficient of skewness to about 10. After that we extract four least significant bits from each variate. The digital part of the described scheme were implemented on FPGA base (Quantum Communications Ltd.). The hardware performs random bits extraction, raw and binary data on-line tests and monitors malfunction. Two devices with different form-factor are produced. The first is an external device with two Ethernet ports. The random data rate obtained by using this device is about 200 Mbps. The second device is an embedded module with LVDS lines for data output. The throughput of the embedded device is about 240 Mbps. A comprehensive statistical analysis of generated bits sequences performed by means of three standard tests of randomness (ENT, Diehard and NIST) widely used in practice for evaluation of the quality of random sequences shows no weakness. Besides, for continuously generated random-bits sequences of 20 Gb length we obtained that the statistical bias is of the order of 10 and the maximal serial autocorrelation coefficient does not exceed 3×10 which attest a high quality of the obtained random-bits sequences. [1] V.N. Chizhevsky, “Fast generation of random bits based on polarization noises in a semiconductor vertical-cavity laser,” Optics and Spectroscopy, vol. 111, pp. 689-694, 2011. [2] V.N. Chizhevsky, “Symmetrization of single-sided or nonsymmetrical distributions: The way to enhance a generation rate of random bits from a physical source of randomness,” Phys. Rev. E, vol. 82, pp. 050101-4, 2010. The work was supported by leading Universities of Russian Federation (grant