Efficient and reliable Random Number Generator (RNG) are increasingly demanded in cryptographic applications, such as on-the-fly data encription/decription and as a general tool for data protection. Main requirement of RNG is a true randomness, which is achievable by means of physical randomness sources only. A True-RNG based on two independent Stochastic Processes (SP) is presented and discussed. As primary randomness sources, two radioactive decay processes are used. A radioactive source has many advantages over others noise sources, since the decay rate of any nuclide does not depend on temperature, chemical composition, physical state, environmental conditions, and aging. In addition, in U ore for example, the various nuclides are, at very good approximation, at equilibrium in the decay chain, so that many stationary independent SP's with the same statistics can be simply obtained by detecting and selectively routing, e.g. by pulse amplitude sorting, gamma rays of different energy emitted by different nuclides in the decay chain. Simulation is performed by a numerical code. The random bit stream obtained is tested for randomness by the NIST test suite, and results are shown. A hardware implementation of the system is also presented.
Efficient and reliable Random Number Generator (RNG) are increasingly demanded in cryptographic applications, such as on-the-fly data encription/decription and as a general tool for data protection. Main requirement of RNG is a true randomness, which is achievable by means of physical randomness sources only. A True-RNG based on two independent Stochastic Processes (SP) is presented and discussed. As primary randomness sources, two radioactive decay processes are used. A radioactive source has many advantages over others noise sources, since the decay rate of any nuclide does not depend on temperature, chemical composition, physical state, environmental conditions, and aging. In addition, in U ore for example, the various nuclides are, at very good approximation, at equilibrium in the decay chain, so that many stationary independent SP's with the same statistics can be simply obtained by detecting and selectively routing, e.g. by pulse amplitude sorting, gamma rays of different energy emitted by different nuclides in the decay chain. Simulation is performed by a numerical code. The random bit stream obtained is tested for randomness by the NIST test suite, and results are shown. A hardware implementation of the system is also presented.
Random number generators (RNG) are an important resource in many areas: cryptography (both quantum and classical), probabilistic computation (Monte Carlo methods), numerical simulations, industrial testing and labeling, hazard games, scientific research, etc. Because today's computers are deterministic, they can not create random numbers unless complemented with a RNG. Randomness of a RNG can be precisely, scientifically characterized and measured. Especially valuable is the information-theoretic provable RNG (True RNG - TRNG) which, at state of the art, seem to be possible only by use of physical randomness inherent to certain (simple) quantum systems. On the other hand, current industry standard dictates use of RNG's based on free running oscillators (FRO) whose randomness is derived from electronics noise present in logic circuits and which cannot be strictly proven. This approach is currently used in 3-rd and 4-th generation FPGA and ASIC hardware, unsuitable for realization of quantum TRNG. We compare weak and strong aspects of the two approaches and discuss possibility of building quantum TRNG in the recently appeared Mixed Signal FPGA technology. Finally, we discuss several examples where use of a TRNG is critical and show how it can significantly improve security of cryptographic systems.
One key requirement for many cryptograhic schemes is the generation of random numbers.Sequences of random numbers are used at several stages of a standard cryptographic protocol.One simple example is a Vernam cipher, where a string of random numbers is added to message string to generate encrypted code.C = M ⊕ K.It has been mathematically shown that this simple scheme is unbreakable if key K is as long as M and is used only once.The security of a cryptosystem shall not be based on keeping the algorithm secret but solely on keeping the key secret.The security of a random number generator (RNG) is related to the difficulty of predicting its future sequence values from past values.The quality and unpredictability of secret data is critical to securing communication by modern cryptographic techniques.The generation of such data for cryptographic purposes typically requires an unpredictable physical source of random data.We studied a chaotic circuit which consisted of an inductor, capacitance, diode and thus used for the BB84 protocol.We have studied both pseudo random and true random number generators and evaluated them through various tests like frequency, correlation, NIST etc.
In this paper, we present an alternative method of gathering seed data for random number generation (RNG) in cryptographic applications. Our proposed method utilises the inherent randomness of signal data from celestial sources in radio astronomy to provide seeds for RNG. The data sets were collected from two separate celestial sources, and run through the SHA-256 algorithm to deskew the data and produce random numbers with a uniform distribution. The resulting data sets pass all tests in the NIST Statistical Test Suite for random data, with a mean of 98.9% of the 512 total bitstreams from the two sources passing all tests in the NIST suite, as well as further testing in R. These results are on par with the control set generated using Java’s SecureRandom function. An explanation of the sources, the data processing and detailed results of each of the tests are presented.
Even if the output of a Random Number Generator (RNG) is perfectly uniformly distributed, it may be correlated to pre-existing information and therefore be predictable. Statistical tests are thus not sufficient to guarantee that an RNG is usable for applications, e.g., in cryptography or gambling, where unpredictability is important. To enable such applications a stronger notion of randomness, termed "true randomness", is required, which includes independence from prior information. Quantum systems are particularly suitable for true randomness generation, as their unpredictability can be proved based on physical principles. Practical implementations of Quantum RNGs (QRNGs) are however always subject to noise, i.e., influences which are not fully controlled. This reduces the quality of the raw randomness generated by the device, making it necessary to post-process it. Here we provide a framework to analyse realistic QRNGs and to determine the post-processing that is necessary to turn their raw output into true randomness.
In this paper, we design a photonic-based true random number generator (True RNG) which is targeted for cryptographic application .Since all security protocols rely on unpredictability, RNGs for crypto applications must meet stringent requirements. The design employs a single-photon detection to generate a random signal which is useful in producing random output. In contrast with traditionally used of frequency sampler circuitry during bit extraction method, it uses a novel method of randomness extraction based on time interval between two successive random signals. The design comprises an optical setup and extremely compact and digitally random bit extraction circuitry which can be implemented on any advance crypto hardware devices. A NIST statistical test is used to test the randomness of the RNG output and has produced a good result. With the help of this True RNG, the cryptographic implementations can be secure enough from being abused of malicious act.
Random numbers are fundamental elements in different fields of science and technology such as computer simulation like Monte Carlo-method simulation, statistical sampling, cryptography, games and gambling, and other areas where unpredictable results are necessary. Random number generators (RNG) are generally classified as “pseudo”-random number generators (PRNG) and "truly" random number generators (TRNG). Pseudo random numbers are generated by computer algorithms with a (random) seed and a specific formula. The random numbers produced in this way (with a small degree of unpredictability) are good enough for some applications such as computer simulation. However, for some other applications like cryptography they are not completely reliable. When the seed is revealed, the entire sequence of numbers can be produced. The periodicity is also an undesirable property of PRNGs that can be disregarded for most practical purposes if the sequence recurs after a very long period. However, the predictability still remains a tremendous disadvantage of this type of generators. Truly random numbers, on the other hand, can be generated through physical sources of randomness like flipping a coin. However, the approaches exploiting classical motion and classical physics to generate random numbers possess a deterministic nature that is transferred to the generated random numbers. The best solution is to benefit from the assets of indeterminacy and randomness in quantum physics. Based on the quantum theory, the properties of a particle cannot be determined with arbitrary precision until a measurement is carried out. The result of a measurement, therefore, remains unpredictable and random. Optical phenomena including photons as the quanta of light have various random, non-deterministic properties. These properties include the polarization of the photons, the exact number of photons impinging a detector and the photon arrival times. Such intrinsically random properties can be exploited to generate truly random numbers. Silicon (Si) is considered as an interesting material in integrated optics. Microelectronic chips made from Si are cheap and easy to mass-fabricate, and can be densely integrated. Si integrated optical chips, that can generate, modulate, process and detect light signals, exploit the benefits of Si while also being fully compatible with electronic. Since many electronic components can be integrated into a single chip, Si is an ideal candidate for the production of small, powerful devices. By complementary metal-oxide-semiconductor (CMOS) technology, the fabrication of compact and mass manufacturable devices with integrated components on the Si platform is achievable. In this thesis we aim to model, study and fabricate a compact photonic quantum random number generator (QRNG) on the Si platform that is able to generate high quality, "truly" random numbers. The proposed QRNG is based on a Si light source (LED) coupled with a Si single photon avalanche diode (SPAD) or an array of SPADs which is called Si photomultiplier (SiPM). Various implementations of QRNG have been developed reaching an ultimate geometry where both the source and the SPAD are integrated on the same chip and fabricated by the same process. This activity was performed within the project SiQuro—on Si chip quantum optics for quantum computing and secure communications—which aims to bring the quantum world into integrated photonics. By using the same successful paradigm of microelectronics—the study and design of very small electronic devices typically made from semiconductor materials—, the vision is to have low cost and mass manufacturable integrated quantum photonic circuits for a variety of different applications in quantum computing, measure, sensing, secure communications and services. The Si platform permits, in a natural way, the integration of quantum photonics with electronics. Two methodologies are presented to generate random numbers: one is based on photon counting measurements and another one is based on photon arrival time measurements. The latter is robust, masks all the drawbacks of afterpulsing, dead time and jitter of the Si SPAD and is effectively insensitive to ageing of the LED and to its emission drifts related to temperature variations. The raw data pass all the statistical tests in national institute of standards and technology (NIST) tests suite and TestU01 Alphabit battery without a post processing algorithm. The maximum demonstrated bit rate is 1.68 Mbps with the efficiency of 4-bits per detected photon. In order to realize a small, portable QRNG, we have produced a compact configuration consisting of a Si nanocrystals (Si-NCs) LED and a SiPM. All the statistical test in the NIST tests suite pass for the raw data with the maximum bit rate of 0.5 Mbps. We also prepared and studied a compact chip consisting of a Si-NCs LED and an array of detectors. An integrated chip, composed of Si p+/n junction working in avalanche region and a Si SPAD, was produced as well. High quality random numbers are produced through our robust methodology at the highest speed of 100 kcps. Integration of the source of entropy and the detector on a single chip is an efficient way to produce a compact RNG. A small RNG is an essential element to guarantee the security of our everyday life. It can be readily implemented into electronic devices for data encryption. The idea of "utmost security" would no longer be limited to particular organs owning sensitive information. It would be accessible to every one in everyday life.