Recurrence and Polya Number of General One-Dimensional Random Walks

The recurrence properties of random walks can be characterized by P61ya number, i.e., the probability that the walker has returned to the origin at least once. In this paper, we consider recurrence properties for a general 1D random walk on a line, in which at each time step the walker can move to the left or right with probabilities l and r, or remain at the same position with probability o （l ＋ r ＋ o = 1）. We calculate Polya number P of this model and find a simple expression for P as, P = 1 - △, where △ is the absolute difference of l and r （△= ｜l - r｜）. We prove this rigorous expression by the method of creative telescoping, and our result suggests that the walk is recurrent if and only if the left-moving probability l equals to the right-moving probability r.

A Robust Low Power Chaos-Based Truly Random Number Generator

This paper presents a low power,truly random number generator （TRNG） based on a simple chaotic map of the Bernoulli shift,which is extended to remain robustness in implementation. The map is realized by switched-current techniques that can fully integrate it in a cryptosystem on a chip. A pipelined architecture post-processed by a simple XOR circuit is used to improve the entropy. The TRNG is fabricated in an HJTC 0.18μm CMOS mixed signal process,and the statistical properties are investigated by measurement results. The power consumption is only 1.42mW and the truly random output bit rate is 10Mbit/s.

A Hybrid Random Number Generator Using Single Electron Tunneling Junctions and MOS Transistors

This paper proposes a novel single electron random number generator （RNG）. The generator consists of multiple tunneling junctions （MTJ） and a hybrid single electron transistor （SET）/MOS output circuit. It is an oscillator-based RNG. MTJ is used to implement a high-frequency oscillator, which uses the inherent physical randomness in tunneling events of the MTJ to achieve large frequency drift. The hybrid SET and MOS output circuit is used to amplify and buffer the output signal of the MTJ oscillator. The RNG circuit generates high-quality random digital sequences with a simple structure. The operation speed of this circuit is as high as 1GHz. The circuit also has good driven capability and low power dissipation. This novel random number generator is a promising device for future cryptographic systems and communication applications.

A universal algorithm to generate pseudo-random numbers based on uniform mapping as homeomorphism

A specific uniform map is constructed as a homeomorphism mapping chaotic time series into [0,1] to obtain sequences of standard uniform distribution. With the uniform map, a chaotic orbit and a sequence orbit obtained are topologically equivalent to each other so the map can preserve the most dynamic properties of chaotic systems such as permutation entropy. Based on the uniform map, a universal algorithm to generate pseudo random numbers is proposed and the pseudo random series is tested to follow the standard 0-1 random distribution both theoretically and experimentally. The algorithm is not complex, which does not impose high requirement on computer hard ware and thus computation speed is fast. The method not only extends the parameter spaces but also avoids the drawback of small function space caused by constraints on chaotic maps used to generate pseudo random numbers. The algorithm can be applied to any chaotic system and can produce pseudo random sequence of high quality, thus can be a good universal pseudo random number generator.

Strong Law of Large Numbers and Complete Convergence for Sequences of -Mixing Random Variables

We give some theorems of strong law of large numbers and complete convergence for sequences of φ-mixing random variables. In particular, Wittmann＇s strong law of large numbers and Teicher＇s strong law of large nnumbers for independent random variables are generalized to the case of φ -minxing random variables.

Post-processing Free Quantum Random Number Generator Based on Avalanche Photodiode Array

Quantum random number generators adopting single negligible dead time of avalanche photodiodes （APDs） photon detection have been restricted due to the non- We propose a new approach based on an APD array to improve the generation rate of random numbers significantly. This method compares the detectors＇ responses to consecutive optical pulses and generates the random sequence. We implement a demonstration experiment to show its simplicity, compactness and scalability. The generated numbers are proved to be unbiased, post-processing free, ready to use, and their randomness is verified by using the national institute of standard technology statistical test suite. The random bit generation efficiency is as high as 32.8% and the potential generation rate adopting the 32× 32 APD array is up to tens of Gbits/s.

A CLASS OF RANDOM NUMBER GENERATORS BASED ON WEYL SEQUENCE

The generation of good pseudo-random numbers is the base of many important fields in scientific computing, such as randomized algorithms and numerical solution of stochastic differential equations. In this paper, a class of random number generators （RNGs） based on Weyl sequence is proposed. The uniformity of those RNGs is proved theoretically. Statistical and numerical computations show the efficiency of the methods.

Pseudo Random Number Generator Based on Back Propagation Neural Network

Random numbers play an increasingly important role in secure wire and wireless communication. Thus the design quality of random number generator(RNG) is significant in information security. A novel pseudo RNG is proposed for improving the security of network communication. The back propagation neural network(BPNN) is nonlinear, which can be used to improve the traditional RNG. The novel pseudo RNG is based on BPNN techniques. The result of test suites standardized by the U.S shows that the RNG can satisfy the security of communication.

Strong Law of Large Numbers for Array of Rowwise AANA Random Variables

In this article, the strong laws of large numbers for array of rowwise asymptotically almost negatively associated(AANA) random variables are studied. Some sufficient conditions for strong laws of large numbers for array of rowwise AANA random variables are presented without assumption of identical distribution. Our results extend the corresponding ones for independent random variables to case of AANA random variables.

On Strong Law of Large Numbers for Random Sequence

This note is devoted to introduce a new concept of conditionally dominated random variables.Under suitable restrict conditions,a general strong law of large numbers for arbitrary continuous random variables is obtained.

Towards Post-Quantum Cryptography Using Thermal Noise Theory and True Random Numbers Generation

The advent of quantum computers and algorithms challenges the semantic security of symmetric and asymmetric cryptosystems. Thus, the implementation of new cryptographic primitives is essential. They must follow the breakthroughs and properties of quantum calculators which make vulnerable existing cryptosystems. In this paper, we propose a random number generation model based on evaluation of the thermal noise power of the volume elements of an electronic system with a volume of 58.83 cm3. We prove through the sampling of the temperature of each volume element that it is difficult for an attacker to carry out an exploit. In 12 seconds, we generate for 7 volume elements, a stream of randomly generated keys of 187 digits that will be transmitted from source to destination through the properties of quantum cryptography.

LYAPOUNOLYAPOUNOV EXPONENTS AND LAW OF LARGE NUMBERS FOR RANDOM WALK IN RANDOM ENVIRONMENT WITH HOLDING TIMES

In this article, the authors mainly discuss the law of large number under Kalikow＇s condition for multi-dimensional random walks in random environment with holding times. The authors give an expression to the escape speed of random walks in terms of the Lyapounov exponents, which have been precisely used in the context of large deviation.

Parameter analysis of chaotic superlattice true random number source

Superlattices in chaotic state can be used as a key part of a true random number generator. The chaotic characteristics of the signal generated in the superlattice are mostly affected by the parameters of the superlattice and the applied voltage, while the latter is easier to adjust. In this paper, the model of the superlattice is first established. Then, based on this model, the chaotic characteristics of the generated signal are studied under different voltages. The results demonstrate that the onset of chaos in the superlattice is typically accompanied by the mergence of multistability, and there are voltage intervals in each of which the generated signal is chaotic.

Improved quantum randomness amplification with finite number of untrusted devices based on a novel extractor

Quantum randomness amplification protocols have increasingly attracted attention tbr their tantastic ability to ampllI~, weak randomness to almost ideal randomness by utilizing quantum systems. Recently, a realistic noise-tolerant randomness amplification protocol using a finite number of untrusted devices was proposed. The protocol has the composable security against non-signalling eavesdroppers and could produce a single bit of randomness from weak randomness sources, which is certified by the violation of certain Bell inequalities. However, the protocol has a non-ignorable limitation on the min- entropy of independent sources. In this paper, we further develop the randomness amplification method and present a novel quantum randomness amplification protocol based on an explicit non-malleable two independent-source randomness extractor, which could remarkably reduce the above-mentioned specific limitation. Moreover, the composable security of our improved protocol is also proposed. Our results could significantly expand the application range for practical quantum randomness amplification, and provide a new insight on the practical design method for randomness extraction.

A hybrid-type quantum random number generator

This paper proposes a well-performing hybrid-type truly quantum random number generator based on the time interval between two independent single-photon detection signals, which is practical and intuitive, and generates the initial random number sources from a combination of multiple existing random number sources. A time-to-amplitude converter and multichannel analyzer are used for qualitative analysis to demonstrate that each and every step is random. Furthermore, a carefully designed data acquisition system is used to obtain a high-quality random sequence. Our scheme is simple and proves that the random number bit rate can be dramatically increased to satisfy practical requirements.

The Annealed Entropy of Wiener Number on Random Double Hexagonal Chains

We study a random planar honeycomb lattice model, namely the random double hexagonal chains. This is a lattice system with nonperiodic boundary condition. The Wiener number is an important molecular descriptor based on the distances, which was introduced by the chemist Harold Wiener in 1947. By applying probabilistic method and combinatorial techniques we obtained an explicit analytical expression for the expected value of Wiener number of a random double hexagonal chain, and the limiting behaviors on the annealed entropy of Wiener number when the random double hexagonal chain becomes infinite in length are analyzed.

On the Strong Law of Large Numbers for Non-Independent B-Valued Random Variables

This paper investigates some conditions which imply the strong laws of large numbers for Banach space valued random variable sequences. Some generalizations of the Marcinkiewicz-Zygmund theorem and the Hoffmann-J?rgensen and Pisier theorem are obtained. Key words strong law of large numbers - Banach space valued random variable sequence - p-smoothable Banach space CLC number O 211.4 - O 211.6 Foundation item: Supported by the National Natural Science Foundation of China (10071058)Biography: Gan Shi-xin (1939-), male, Professor, research direction: martingale theory, probability limiting theory and Banach space geometry theory.

Biased Random Number Generator Based on Bell's Theorem

We propose a biased random number generation protocol whose randomness is based on the violation of the Clauser Home inequality. Non-maximally entangled state is used to maximize the Bell violation. Due to the rotational asymmetry of the quantum state, the ratio of Os to ls varies with the measurement bases. The experimental partners can then use their measurement outcomes to generate the biased random bit string. The bias of their bit string can be adjusted by altering their choices of measurement bases. When this protocol is implemented in a device-independent way, we show that the bias of the bit string can still be ensured under the collective attack.

Physical generation of random numbers using an asymmetrical Boolean network

Autonomous Boolean networks(ABNs)have been successfully applied to the generation of random number due to their complex nonlinear dynamics and convenient on-chip integration.Most of the ABNs used for random number generators show a symmetric topology,despite their oscillations dependent on the inconsistency of time delays along links.To address this issue,we suggest an asymmetrical autonomous Boolean network(aABN)and show numerically that it provides large amplitude oscillations by using equal time delays along links and the same logical gates.Experimental results show that the chaotic features of aABN are comparable to those of symmetric ABNs despite their being made of fewer nodes.Finally,we put forward a random number generator based on aABN and show that it generates the random numbers passing the NIST test suite at 100 Mbits/s.The unpredictability of the random numbers is analyzed by restarting the random number generator repeatedly.The aABN may replace symmetrical ABNs in many applications using fewer nodes and,in turn,reducing power consumption.

Design of Hybrid True Random Number Generator for Cryptographic Applications

In real-time applications,unpredictable random numbers play a major role in providing cryptographic and encryption processes.Most of the existing random number generators are embedded with the complex nature of an amplifier,ring oscillators,or comparators.Hence,this research focused more on implementing a Hybrid Nature of a New Random Number Generator.The key objective of the proposed methodology relies on the utilization of True random number generators.The randomness is unpredictable.The additions of programmable delay lines will reduce the processing time and maintain the quality of randomizing.The performance comparisons are carried out with power,delay,and lookup table.The proposed architecture was executed and verified using Xilinx.The Hybrid TRNG is evaluated under simulation and the obtained results outperform the results of the conventional random generators based on Slices,area and Lookup Tables.The experimental observations show that the proposed Hybrid True Random Number Generator(HTRNG)offers high operating speed and low power consumption.