Random number generators are indispensable for a multi- tude of tasks; from electronic games to secure communications. Most gen- erators have been made either in software or determinist hardwired de- vices such as the Linear-Feedback-Shift-Registers; while gaining in costs or speed, the “random” sequences generated are actually deterministic, obeying clear generating algorithms, despite all randomness appearance of their outputs. From the other side, Nature presents a multitude of sources of true randomness that can be explored. Commercial random generators exist based on physical processes as the source of randomness. Difficulties are always present to extract Nature’s randomness. This paper presents guidelines for construction of a fast (telecommunication speed) Physical Random Number Generator. It discusses the fundamental physical ele- ments involved, technicalities of signal recording and its limitations, and the final bit extraction. The need for randomness tests is emphasized and the impossibility of guaranteeing true randomness of a finite sequence is discussed.
Random number generators are indispensable for a multi- tude of tasks; from electronic games to secure communications. Most gen- erators have been made either in software or determinist hardwired de- vices such as the Linear-Feedback-Shift-Registers; while gaining in costs or speed, the “random” sequences generated are actually deterministic, obeying clear generating algorithms, despite all randomness appearance of their outputs. From the other side, Nature presents a multitude of sources of true randomness that can be explored. Commercial random generators exist based on physical processes as the source of randomness. Difficulties are always present to extract Nature’s randomness. This paper presents guidelines for construction of a fast (telecommunication speed) Physical Random Number Generator. It discusses the fundamental physical ele- ments involved, technicalities of signal recording and its limitations, and the final bit extraction. The need for randomness tests is emphasized and the impossibility of guaranteeing true randomness of a finite sequence is discussed.
Random numbers (RNs) have applications in many areas: lottery games, gambling, computer simulation, and, most importantly, cryptography [N. Gisin et al., Rev. Mod. Phys. 74 (2002) 145]. In cryptography theory, the theoretical security of the system calls for high quality RNs. Therefore, developing methods for producing unpredictable RNs with adequate speed is an attractive topic. Early on, despite the lack of theoretical support, pseudo RNs generated by algorithmic methods performed well and satisfied reasonable statistical requirements. However, as implemented, those pseudorandom sequences were completely determined by mathematical formulas and initial seeds, which cannot introduce extra entropy or information. In these cases, “random” bits are generated that are not at all random. Physical random number generators (RNGs), which, in contrast to algorithmic methods, are based on unpredictable physical random phenomena, have attracted considerable research interest. However, the way that we extract random bits from those physical entropy sources has a large influence on the efficiency and performance of the system. In this manuscript, we will review and discuss several randomness extraction schemes that are based on radiation or photon arrival times. We analyze the robustness, post-processing requirements and, in particular, the extraction efficiency of those methods to aid in the construction of efficient, compact and robust physical RNG systems.
One of the main problems in the construction of quantum random number generators Ð obtainment of a provably random output sequence from physical measurements, i.e., from an initial sequence generated by a physical random number generator Ð is investigated.The conceptual feasibility and the conditions under which randomness can be `reached,' as well as the meaning of the `provable randomness' term, are discussed.We consider the methods of extracting provably random bit sequences from stationary Markov chains of finite order, i.e., under the assumption of the finite depth of the dependence of the results of physical measurements on the prehistory, which is an adequate approximation of the real situation.The extraction of the output provably random bit sequence from the initial sequence of the results of physical measurements using V F Babkin's effective arithmetic coding method is demonstrated.It is shown that random bit sequences can be provably obtained even from primary sequences of the results of physical measurements, which are dependent on (correlated to) any finite depth (prehistory).We aim to reveal the connection of various approximations employed in the development and description of methods for obtaining random bit sequences with the basic physical limitations of Nature.The mathematical proofs are detailed to the level of practical algorithms applied in real random number generators.The necessary mathematical propositions are presented at an intuitive level for physicists, do not require prior knowledge in this area, and are comprehensible to undergraduate university students.
Random numbers have great application value in the fields of secure communications, which are commonly used as secret keys to encrypt the information. To guarantee that the information is absolutely secure in the current high-speed communication, the applied random keys should possess a generation speed not less than the encrypted data rate, according to one-time pad theory found by Shannon (Shannon C E 1949 Bell.Syst.Tech.J. 28 656) Pseudo-random numbers generated by algorithm may easily reach a fast speed, but a certain periodicity makes them difficult to meet the aforementioned demand of information security. Utilizing physical stochastic phenomena can provide reliable random numbers, called physical random number generators (RNGs). However, limited by the bandwidth of the conventional physical sources such as electronic noise, frequency jitter of oscillator and quantum randomness, the traditional physical RNG has a generation speed at a level of Mb/s typically. Therefore, real-time and ultrafast physical random number generation is urgently required from the view of absolute security for high-speed communication today. With the advent of wideband photonic entropy sources, in recent years lots of schemes for high-speed random number generation are proposed. Among them, chaotic laser has received great attention due to its ultra-wide bandwidth and large random fluctuation of intensity. The real-time speed of physical RNG based on chaotic laser is now limited under 5 Gb/s, although the reported RNG claims that an ultrafast speed of Tb/s is possible in theory. The main issues that restrict the real-time speed of RNG based on chaotic laser are from two aspects. The first aspect is electrical jitter bottleneck confronted by the electrical analog-to-digital converter (ADC). Specifically, most of the methods of extracting random numbers are first to convert the chaotic laser into an electrical signal by a photo-detector, then use an electrical ADC driven by radio frequency (RF) clock to sample and quantify the chaotic signal in electronic domain. Unfortunately, the response rate of ADC is below Gb/s restricted by the aperture jitter (several picoseconds) of RF clock in the sample and hold circuit. The second aspect comes from the complex post-processes, which are fundamental in current RNG techniques to realize a good randomness. The strict synchronization among post-processing components (e.g., XOR gates, memory buffers, high-order difference) is controlled by an RF clock. Similarly, it is also an insurmountable obstacle to achieve an accurate synchronization due to the electronic jitter of the RF clock. In this paper, we propose a method of ultrafast multi-bit physical RNG based on chaotic laser without any post-process. In this method, a train of optical pulses generated by a GHz mode-locked laser with low temporal jitter at a level of fs is used as an optical sampling clock. The chaotic laser is sampled in the optical domain through a low switching energy and high-linearity terahertz optical asymmetric demultiplexer (TOAD) sampler, which is a fiber loop with an asymmetrical nonlinear semiconductor optical amplifier. Then, the peak amplitude of each sampled chaotic pulse is digitized by a multi-bit comparator (i.e., a multi-bit ADC without sample and hold circuit) and converted into random numbers directly. Specifically, a proof-of-principle experiment is executed to demonstrate the aforementioned proposed method. In this experiment, an optical feedback chaotic laser is used, which has a bandwidth of 6 GHz. Through setting a sampling rate to be 5 GSa/s and selecting 4 LSBs outputs of the 8-bit comparator, 20 Gb/s (=5 GSa/s4 LSBs) physical random number sequences are obtained. Considering the ultrafast response rate of TOAD sampler, the speed of random numbers generated by this method has the potential to reach several hundreds of Gb/s as long as the used chaotic laser has a sufficient bandwidth.
Abstract The nature of randomness and constructive and provable methods to obtain (extract) it from observations of physical systems are discussed. True randomness, which exists only in a microcosm in the quantum-mechanical description of physical systems, is a fundamental property of quantum systems, which manifests itself in the outcomes of measurements upon quantum systems. The classical description of physical systems does not include any randomness and, in fact, it is introduced ‘manually’ by means of uncertainty — unknown initial conditions. Methods to really ‘feel’ quantum randomness are discussed using the example of a quantum device, a random number generator. Issues related to the ‘proof’ of randomness — testing of numerical sequences — are reviewed, and logical constructions that underlie such testing are analyzed. A mathematical apparatus is used to this end, which does not require special academic training, so standard knowledge from university courses on quantum mechanics and probability theory is sufficient. The authors aim to track a unified logical path from the origin of randomness in the quantum domain to its extraction, physical implementation, and testing.
Generation of random numbers is a central problem for many applications in the field of information processing, including, e.g., cryptography, in classical and quantum regime, but also mathematical modeling, Monte Carlo methods, gambling and many others. Both, the quality of the randomness and efficiency of the random numbers generation process are crucial for the most of these applications. Software produced pseudorandom bit sequences, though sufficiently quick, do not fulfill required randomness quality demands. Hence, the physical hardware methods are intensively developed to generate truly random number sequences for information processing and electronic security application. In the present paper we discuss the idea of the quantum random number generators. We also present a variety of tests utilized to assess the quality of randomness of generated bit sequences. In the experimental part we apply such tests to assess and compare two quantum random number generators, PQ4000KSI (of company ComScire US) and JUR01 (constructed in Wroclaw University of Science and Technology upon the project of The National Center for Research and Development) as well as a pseudorandom generator from the Mathematica Wolfram package. Finally, we present our new prototype of fully operative miniaturized quantum random generator JUR02 producing a random bit sequence with velocity of 1 Mb/s, which successfully passed standard tests of randomness quality (like NIST and Dieharder tests). We also shortly discuss our former concept of an entanglement-based quantum random number generator protocol with unconditionally secure public randomness verification.
We propose what we believe to be a new approach to nondeterministic random-number generation. The randomness originated from the uncorrelated nature of consecutive laser pulses with Poissonian photon statistics and that of photon number detections is used to generate random bit, and the von Neumann correction method is used to extract the final random bit. This method is proved to be bias free in randomness generation, provided that the single photon detections are mutually independent. Further, it has the advantage in fast random bit generation, since no postprocessing is needed. A true random-number generator based on this method is realized, and its randomness is tested and guaranteed using three statistical test batteries.