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Optical Engineering

Physical-random number generation using white frequency-modulation noise of frequency-stabilized semiconductor lasers

Tomoyuki Uehara, Takashi Satō

Published Apr 1, 2009• 1 citation
Publisher

Abstract

Precisely frequency-stabilized semiconductor lasers produce physical-random numbers, allowing for optimal noise-suppression with one notable exception: white frequency-modulation (FM) noise. However, this component can also be converted into physical-random numbers. The interference created between two beams of rubidium (Rb) gas-cell-stabilized lasers allows for laser frequency noise to be extracted. Using this technique, we produce physical-random numbers from the relative frequency noise. Finally, we confirm that the numbers produced are, in fact, random, by means of the standard National Institute of Standards and Technology Federal Information Processing Standard (NIST FIPS) 140-2 test.

DOI
10.1117/1.3123483

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Precisely frequency-stabilized semiconductor lasers produce physical-random numbers, allowing for optimal noise-suppression with one notable exception: white frequency-modulation (FM) noise. However, this component can also be converted into physical-random numbers. The interference created between two beams of rubidium (Rb) gas-cell-stabilized lasers allows for laser frequency noise to be extracted. Using this technique, we produce physical-random numbers from the relative frequency noise. Finally, we confirm that the numbers produced are, in fact, random, by means of the standard National Institute of Standards and Technology Federal Information Processing Standard (NIST FIPS) 140-2 test.
Abstract Diode Lasers (DLs) are influenced by fast frequency noise stemming from fluctuations in spontaneous emissions, a phenomenon that is of great use when generating fast physical-random numbers. This paper describes a physical-random number generator that uses a DLs frequency noise and rubidium (Rb) absorption lines as frequency noise sources and frequency discriminators. This device actually produced physical-random numbers at a rate of 500 megabits per second, but it depends on the relation between the DL frequency noise and frequency discriminator characteristics. This relation is investigated and the conditions for physical-random number generation are explained.
We describe a method of generating physical random numbers by means of a diode laser that has an extremely wide-band frequency-noise profile. Fluctuations in the laser frequency affect the intensity of the light transmitted through the optical frequency discriminator, detected thereafter as random fluctuations. This allows us to simultaneously generate 8 random bit streams, due to the parallel processing of 8-digit binary numbers sampled by an 8-bit analog-to-digital converter. Finally, we generated physical random numbers at a rate of 3 Gbit/s, by combining one data stream with another stream that is delayed by 2 ms, by exclusive-OR.
In the communication through the network, it is essential to encrypt information to secure safety of the communication. An encryption method used for communication is a public key cryptosystem and a hybrid cryptosystem that put a public key cryptosystem and a private-key cryptosystem together mainly now. The safe grounds of these methods are to need vast calculation time to decode private key from a public key, but, by a cloud computing using the network accomplishing rapid progress and the development of the study of a quantum computer, the safe securing of information security by the cryptographic technology is becoming difficult for these past several years. One method to solve this problem includes quantum cryptography communication technology using a quantum key distribution. Because the quantum communication can detect the wiretapping on the channel, we can realize complete secret communication by letting both transmission and reception believers share private key. The randomness of the private key (i.e., the random number for secret codes) becomes important to assure the safety of this technique. Therefore the development of the technique that can generate chaotic random numbers (i.e., physical random number) fast becomes the urgent need. This thesis focuses on a very high-speed frequency noise of the laser diode to generate a physical random number fast, and assumed this frequency noise as a source for physical random number generation. We detected a high-speed frequency noise of the laser diode as a fluctuation of the transmitted light intensity using a frequency discriminator. This principle is the same as a principle of slope detection which is a kind of the demodulation technology in the FM communication. We used a Fabry-Perot type laser diode of wavelength 780nm for a noise source, and the D_2 absorption line of the rubidium atom for a frequency discriminator. We converted a transmitted light intensity signal into binary data by an A/D converter, and produced the binary physical random number sequences by extracting binary sequence from binary data. Generated physical random number sequences are statistically confirmed its quality by means of a de facto standard “NIST SP800-22” of the random number test for the secret code. Physical random number sequences are generated from binary data by two methods. The first method produced random number sequences per digits using least significant bits of binary data obtained from the A/D converter of vertical resolution 8 bits in parallel. The second method produced the binary random number sequence by connecting the data of each digit of binary data to one. We can make the generation speed of the physical random number sequence faster than the sampling speed of the A/D converter by using these methods. And, the operation such as performing EX-OR (XOR) between different random numbers is necessary for using it as a random number for the code because the physical random number usually has bad equal probability characteristics. The method called the Reverse XOR method that developed this XOR operation is recently suggested to improve the generation speed of the physical random number in other precedent studies. In this study, both this Reverse XOR and the normal XOR (XOR method) methods are used for generating a physical random number. And, a physical random number sequence generating speed of 120 Gb/s was confirmed by a method of generating random number sequences from several digits of 8-bits-binary-data in parallel. In addition, Improved XOR and Improved Reverse XOR methods proposed in this thesis generated the physical random number sequence faster than the normal XOR and the Reverse XOR methods. As a result, this thesis reported that a physical random number sequence was generated at 160 Gb/s. The relations between the frequency discriminator and the oscillation frequency of the laser diode bring big influence in the quality of the physics random number in our physical random number generation method. This is because frequency properties of the detected noise signal will change by the relation between the slant of the frequency discriminator and the frequency of the laser diode. Therefore the relation between the frequencies of the oscillation spectrum of this laser diode and the frequency discriminator was investigated, and the most suitable condition for generating a physical random number was discussed. In addition, the oscillation frequency of the laser diode greatly changes by a fluctuation of the environment temperature and the driving current. Therefore it is necessary to stabilize and control the oscillation frequency of the laser diode to the limited area within the absorption line of the rubidium atom in order to generate a physical random number stably for a long time. Therefore the oscillation frequency of the laser diode was controlled by using a technique of Phase-locked-Loop to the frequency of the slope of the rubidium atom absorption curve.
An inordinate amount of time, effort (and paper) has been spent trying to find a way to stabilize laser-diode frequencies, but our research team has been working on the premise, that frequency instability can, in fact, have its up-sides. In the present work, we focus on a method that uses laser diodes’ own noise to generate physical random numbers. Introducing a frequency discriminator as a reference, we control and stabilize the difference between the frequency reference and the laser frequency, thereby generating random numbers at a suitable point.
Not so long ago, pseudo random numbers generated by numerical formulae were considered to be adequate for encrypting important data-files, because of the time needed to decode them. With today’s ultra high-speed processors, however, this is no longer true. So, in order to thwart ever-more advanced attempts to breach our system’s protections, cryptologists have devised a method that is considered to be virtually impossible to decode, and uses what is a limitless number of physical random numbers. This research describes a method, whereby laser diode’s frequency noise generate a large quantities of physical random numbers. Using two types of photo detectors (APD and PIN-PD), we tested the abilities of two types of lasers (FP-LD and VCSEL) to generate random numbers. In all instances, an etalon served as frequency discriminator, the examination pass rates were determined using NIST FIPS140-2 test at each bit, and the Random Number Generation (RNG) speed was noted.