Mieczyslaw Jessa

The period of sequences generated by tent-like maps

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.

Designing security for number sequences generated by means of the sawtooth chaotic map

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.

Enhancing the Randomness of a Combined True Random Number Generator Based on the Ring Oscillator Sampling Method

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.

Data encryption algorithms using one-dimensional chaotic maps

In the paper we consider the possibility of using one dimensional chaotic maps (1D maps) in traditional secret-key cryptography. We propose encryption and decryption algorithms which use the properties of 1D chaotic maps defined for initial points being rational numbers.

The use of delay lines in a ring-oscillator-based combined true random number generator

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.

On the Quality of Random Sequences Produced with a Combined Random Bit Generator

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.

High-Speed FPGA-Based Pseudorandom Generators with Extremely Long Periods

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.

Hardware and software realization of time error measurements with real-time assessment of ADEV, TDEV, and MTIE

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.

Discrete-time phase-locked loop as a source of random sequences with different distributions

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.

A novel method of blind signal detection using the distribution of the bin values of the power spectrum density and the moving average

Abstract Signal detection in additive white Gaussian noise (AWGN) is one of the long-term developments driving the evolution of many different fields of science and technology, with important applications in telecommunications, medicine and astronomy. In this paper, we propose a novel method of blind signal detection that does not require knowledge of the noise variance. This method uses the distribution of the bin values of the power spectrum density of the received signal and the moving average (MAV). The simulation results for radio pulses show that the spectrum sensing performance is significantly improved under the proposed scheme compared to that of known blind signal detection methods.