[Show abstract][Hide abstract] ABSTRACT: In this paper, we propose a novel method for increasing the entropy of a sequence of independent, discrete random variables with arbitrary distributions. The method uses an auxiliary table and a novel theorem that concerns the entropy of a sequence in which the elements are a bitwise exclusive-or sum of independent discrete random variables.
[Show abstract][Hide abstract] ABSTRACT: In this paper, we prove that a combined binary generator, which combines modulo-2 bit streams produced by independent generators or by generators that can be grouped into independent pairs of dependent generators, can provide unbiased and uncorrelated bit streams. This result was obtained under the realistic assumption that each source generator produces a sequence of correlated and biased bits. The proposed theorems and formulas are useful in designing random bit generators with satisfactory properties that are robust to external manipulations or to environmental changes up to a certain degree.
No preview · Article · Mar 2015 · IEEE Transactions on Computers
[Show abstract][Hide abstract] ABSTRACT: In this paper, we propose a novel method for producing secure pseudorandom sequences with combined multiplicative congruential generators that have been defined recently. The specific properties of field programmable gate arrays (FPGA) and the combined multiplicative congruential generators enable the generation of secure sequences in only three cycles of the system clock. The output bit rate of the described design, which is composed of eight generators, achieves 1.227 Gbit/s, and this rate can be significantly increased with more generators. In practice the output throughput is limited only by the available resources of the FPGA used in the design.
[Show abstract][Hide abstract] ABSTRACT: This paper presents a novel approach for the design of ring oscillators in a combined true random number generator (TRNG). We propose using delay elements made on carry4 primitives instead of series of inverters or latches in ring oscillators, which enables the construction of many high frequency ring oscillators with different nominal frequencies in the same field programmable gate array (FPGA). The output sequences produced by this type of TRNG pass all NIST 800-22 statistical tests for smaller numbers of ring oscillators than the constructions described in the literature. To assess the unpredictability of the output bits, the restarts mechanism, proposed in earlier papers, was used. Due to the number of ROs with different nominal frequencies and the method of construction of carry4 primitives, it is expected that the proposed TRNG is less sensitive to frequency injection attacks.
[Show abstract][Hide abstract] ABSTRACT: In this paper, we propose a new secure pseudorandom number generator that can be integrated with an arbitrary cryptographic system in the same field programmable gate array (FPGA). The described design uses the Improved Multiplicative Congruential Generators (IMCGs) defined recently. The specific properties of FPGAs and the IMCGs enable the generation of random numbers in only three cycles of the system clock. The output bit rate for eight IMCGs is 2.604 Gbit/s. It can be significantly increased using more IMCGs. The proposed generator can also produce secure bits as a specialized chip, which further increases the output bit rate.
[Show abstract][Hide abstract] ABSTRACT: An efficient method for generating number sequences that pass all statistical tests is combining numbers produced by many independent generators. Excellent statistical properties are very important in many applications but they are not sufficient in cryptography. We need the unpredictability of numbers that ensures the irreproducibility of sequences by an attacker. This paper proposes a new method for enhancing the randomness of a combined true random number generator (TRNG) using jitter observed in ring oscillators (ROs). To enhance the quality of output streams, we use an auxiliary source of randomness (ASR) that perturbs signals produced by ROs. The increase of entropy is obtained by combining XOR bits produced by many biased RO-based TRNGs. It increases the degree of unpredictability but requires a measure of the quality of this process, which is different from statistical testing of time sequences. To assess the unpredictability of output bits, we used the restarts mechanism proposed in earlier papers.
[Show abstract][Hide abstract] ABSTRACT: In this paper, we propose the use of a field programmable gate array (FPGA) to construct high-speed pseudorandom generators with extremely long periods of generated number sequences. The output streams pass all statistical tests from the NIST 800-22 statistical test suite. The numbers are encoded using only 31 bits. We show that by implementing many generators in a single FPGA, a new source of pseudorandom sequences with extremely long periods can be obtained. This source produces sequences that pass the NIST 800-22 statistical tests and the bit rate of the output stream is k times greater, where k is the number of 31-bit generators used. The upper limit of the bit rate depends on the number of 31-bit generators that produce streams passing all NIST 800-22 statistical tests. Although the new generator is not secure, it can be used in cryptography if an auxiliary source of pseudorandom numbers is implemented in the same FPGA.
[Show abstract][Hide abstract] ABSTRACT: This paper deals with the problem of generation of 1-pps timing signal at the output of computer interface controlled by Network Time Protocol. The methods of synchronization of internal computer clock and transmission of the timing signal to the serial interface are described. The results of the measurement of obtained signals are presented. I. INTRODUCTION In the world facing the technological development, the demand for sources of time signals has been still increasing. Currently, numerous systems which to a high extent meet the needs of the consumers of time signals in every respect are offered. The basic sources of time signal are radio systems, for example DCF-77, information systems, i.e. NTP, and satellite systems like GPS. The offered quality of time signal sources falls into the range of tens of milliseconds for radio sources through hundreds of microseconds for NTP to tens of nanoseconds for satellite systems. It seems that the time signal from the Internet has the broadest application because it is easy to acquire and includes a considerable potential for improving its parameters (5, 6, 8). The research presented hereby is, therefore, aimed at the application of NTP protocol to generate the timing signal, with a possibility of utilizing the signal outside the Internet network. It was also assumed that the source of signal would be an ordinary computer with an internal quartz clock. This is an important assumption because the utilization of rubidium clock in the NTP receiver would remove a majority of quality problems affecting the acquired time signal, at the expense, however, of a considerable increase in the device price. Generation of timing signal controlled by NTP could be useful in order to provide some systems with timing signal when we haven't access to good quality timing signal source like atomic clock or GPS controlled oscillator. The authors of this paper have proposed a method of generation of physical timing signal controlled by the NTP (1, 2). In this paper the method enabling generation of physical timing signal (in the form of 1-pps pulses), controlled by the NTP and brought out using serial port of the computer, is described. The algorithm of control of timing signal using NTP protocol is presented and described. The timing signals obtained were compared with the reference signal controlled by GPS receiver.
[Show abstract][Hide abstract] ABSTRACT: Combining random numbers produced by many independent generators can significantly improve the statistical properties of the output sequence. This statement is true for deterministic and non-deterministic sources of random numbers. In cryptography, a user often needs sequences with very good statistical properties but originating from a non-deterministic system. In this paper, we present the results of statistical tests and a new method for distinguishing pseudo and true randomness for sequences produced by a combined true random number generator (TRNG). The generator uses ring oscillators with outputs sampled by a signal of another clock. The combined TRNG was realized in a field programmable gate array (FPGA) produced by Xilinx.
[Show abstract][Hide abstract] ABSTRACT: In this paper, the measuring system SP-4000, which allows for the analysis of timing signals in telecommunication networks, has been described briefly. The solutions that make possible the cooperation between time error meters of this system and the real-time assessment of the parameters have been described. Because of the limitations of computer technology, the user can choose real-time computation for only a single channel. The current version does not allow simultaneous traditional computations and real-time computations. We expect that in the future such computations will be possible for channels that are not chosen for real-time assessment of ADEV, TDEV, and MTIE. We also plan to increase the number of channels capable of real-time computations.
[Show abstract][Hide abstract] ABSTRACT: Summarizing all the series of 24-hours and weekly tests, the authors observed some common tendencies. Neither the server stability nor the speed of generating responses were significantly affected by the fact whether a given test day was a working day or not. It was not confirmed that the server with the shortest time for generating responses is at the same time the most stable one. The influence of the stratum level of the server cannot be noticed, and sometimes a server with better stratum shows worse results. Statistically, the response times of servers are within the range of 100μs.
[Show abstract][Hide abstract] ABSTRACT: Purpose – The purpose of this paper is to demonstrate new properties of continuous- and discrete-time dynamical systems. Design/methodology/approach – First, definitions of two types of spatial symmetry are introduced. These are used as definitions, which, along with existing knowledge show that it is possible to identify properties of dynamical systems that were previously unknown. Findings – The main result of the paper is a new theorem regarding new properties of continuous- and discrete-time dynamical systems. Research limitations/implications – The present study provides a starting point for further research on the differences between continuous- and discrete-time dynamical systems. This work builds on the definition of spatial symmetry. Practical implications – The theorem proved in this paper and the new properties of dynamical systems can be used to introduce new methods of approximating continuous-time dynamical systems by discrete-time dynamical systems and vice versa. Such approaches can also be helpful in constructing chaotic sources to model noise. Originality/value – This paper offers contributions to the broader discussion of differences between continuous- and discrete-time dynamical systems. In particular, the paper supports the statement that many discrete-time processes cannot be embedded into continuous ones.
[Show abstract][Hide abstract] ABSTRACT: A new method to improve the statistical properties of number sequences generated by maximum-period nonlinear congruential generators derived from the Renyi chaotic map is proposed. The characteristic feature of the method is the simultaneous usage of numbers generated by the Renyi map implemented in a finite-state machine, and symbols generated by the same map. The period of sequences generated can be significantly longer than the period of sequences produced by previously defined generators using the same map. It is shown that output sequences obtained with the proposed method can pass all, or almost all, statistical tests from the standard NIST 800-22 statistical test suite for many integer or non-integer values of the parameter.
[Show abstract][Hide abstract] ABSTRACT: This paper presents a new method for improving the statistical properties of sequences generated by the sawtooth chaotic map realized in a finite-state machine in the modular arithmetic. It is shown that sequences obtained with the use of the proposed method pass all tests from the standard NIST 800-22 statistical test suite v.1.8.
[Show abstract][Hide abstract] ABSTRACT: In the paper, we describe how to design the security of number sequences generated by a generator, exploiting the concept of partition of the state space of the sawtooth chaotic map into disjoint subspaces. We prove that the generator can generate nonperiodic and periodic sequences with arbitrary order of elements when the map is implemented in an uncountable set, and periodic sequences with arbitrary order of elements when the map is implemented in a countable set. The numerical security of the generated sequences is shown to be comparable when we limit our observations to finite time intervals. A method of designing the security of sequences produced by the generator was proposed. It was also demonstrated that the existence of methods for reconstructing the linear congruential generator does not imply automatic reconstruction of the generator, exploiting the concept of partition of the state space of the sawtooth map implemented in a finite-state machine.
No preview · Article · Jun 2006 · Circuits and Systems I: Regular Papers, IEEE Transactions on
[Show abstract][Hide abstract] ABSTRACT: In the paper we propose formulas for direct generation of numbers with given distributions: the exponential distribution, the Gaussian distribution, the Cauchy distribution and the Rayleigh distribution. The method we have used combines the inversion method of computing non-uniformly distributed numbers and the topological conjugacy between the non-linear map and the tent map being a chaotic map. The distributions obtained in computer experiment were verified by means of chi-square test.
[Show abstract][Hide abstract] ABSTRACT: In the paper we propose a new algorithm of data encryption, exploiting maps, also chaotic, of the unit interval. We consider the finite-state implementation of the systems, e.g. in computers. The characteristic feature of the algorithm is the possibility of adjusting security of data to be transmitted by means of the security index and the usage of chaos-based pseudorandom number generators as the source of running encryption keys. The algorithm enables fast encryption of those parts of data, which do not require high security. The change in encryption speed is achieved without any change of the length of encryption key, which can be fixed and constant during transmission. It is a distinguishing feature of the proposed system as compared to existing schemes.
[Show abstract][Hide abstract] ABSTRACT: In brief, we describe how to use knowledge about the sequence
period generated by the linear multiplicative congruential generator of
pseudorandom number sequences to determine the sequence period generated
by continuous piecewise-linear chaotic maps of the unit interval or by
maps topologically conjugate to these maps. The method exploits a
relation between a continuous piecewise-linear map and a
piecewise-linear but noncontinuous map of the unit interval with
uniformly distributed extrema points, as well as the fact that the
latter map can be considered as the generalization of the map describing
the linear multiplicative congruential generator
No preview · Article · Feb 2002 · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications
[Show abstract][Hide abstract] ABSTRACT: In the paper we consider the usage of the discrete-time phase-locked loop (DT-PLL) as a source of random sequences with different distributions. The proposed approach enables relatively simple and very fast generation of random sequences with different distributions by chaotic maps topologically conjugate to the sawtooth map. The sequences can be obtained directly or indirectly, i.e. from uniformly distributed sequences, also generated in the real circuit of DT-PLL.
[Show abstract][Hide abstract] ABSTRACT: The basic statistical properties of sequences generated by
sawtooth maps and tent-like maps as a function of parameter determining
the Kolmogorov-Sinai entropy are considered. The statistical properties
of sequences generated by both maps for the same value of parameter and
the same initial point are also compared. It has been also shown that
tent-like maps may have a serious drawback from the perspective of their
application as a source of pseudorandom sequences: they cannot generate
the maximal-length sequences