Statistical Test Suite Research Articles

CONTROLLED HENON SYSTEM AND ITS CRYPTOGRAPHIC APPLICATIONS

This paper proposes a modification of the controlled chaotic Henon system suggested in [Li et al., 2004]. The dynamics of the proposed and existing 2-D systems are analyzed and new chaotic attractors are found in them. We show that these systems exhibit chaotic behavior for a wide range of control parameters. We also construct a chaotic modulation scheme with feedback based on a single controlled chaotic Henon system for use in cryptographic applications. The efficiency of this communication scheme is analyzed and is shown to provide a high level of security, resulting from the proper use of controllers. Furthermore, we propose a technique for generating random-like binary digits from the suggested controlled chaotic Henon systems. Unlike binary digits generated by chaotic Henon systems which usually do not possess random-like properties, the digits generated here are shown (numerically using the NIST statistical test suite) to possess excellent random-like properties. Furthermore, the generated bit sequences are demonstrated to have a large period, which may have useful applications in cryptography.

Statistical tests for associations between two directed acyclic graphs.

Biological data, and particularly annotation data, are increasingly being represented in directed acyclic graphs (DAGs). However, while relevant biological information is implicit in the links between multiple domains, annotations from these different domains are usually represented in distinct, unconnected DAGs, making links between the domains represented difficult to determine. We develop a novel family of general statistical tests for the discovery of strong associations between two directed acyclic graphs. Our method takes the topology of the input graphs and the specificity and relevance of associations between nodes into consideration. We apply our method to the extraction of associations between biomedical ontologies in an extensive use-case. Through a manual and an automatic evaluation, we show that our tests discover biologically relevant relations. The suite of statistical tests we develop for this purpose is implemented and freely available for download.

Assessing the Quality of Pseudo-Random Number Generators

In this article, we describe a new yet simple statistical procedure to better assess the quality of pseudo-random number generators. The new procedure builds on the statistical test suite proposed by the National Institute of Standards and Technology (NIST) and is especially useful for applications in economics. Making use of properties of the binomial distribution, we estimate the conjoint significance level of the test. We apply the proposed procedure to several well-known pseudo-random number generators, and the results confirm its effectiveness.

OVERVIEW OF THE KEPLER SCIENCE PROCESSING PIPELINE

The Kepler Mission Science Operations Center (SOC) performs several critical functions including managing the ~156,000 target stars, associated target tables, science data compression tables and parameters, as well as processing the raw photometric data downlinked from the spacecraft each month. The raw data are first calibrated at the pixel level to correct for bias, smear induced by a shutterless readout, and other detector and electronic effects. A background sky flux is estimated from ~4500 pixels on each of the 84 CCD readout channels, and simple aperture photometry is performed on an optimal aperture for each star. Ancillary engineering data and diagnostic information extracted from the science data are used to remove systematic errors in the flux time series that are correlated with these data prior to searching for signatures of transiting planets with a wavelet-based, adaptive matched filter. Stars with signatures exceeding 7.1 sigma are subjected to a suite of statistical tests including an examination of each star's centroid motion to reject false positives caused by background eclipsing binaries. Physical parameters for each planetary candidate are fitted to the transit signature, and signatures of additional transiting planets are sought in the residual light curve. The pipeline is operational, finding planetary signatures and providing robust eliminations of false positives.

Modified self-shrinking generator

The self-shrinking generator SSG, an elegant keystream generator proposed by Meier and Staffelbach, is built up from a single n-stage primitive linear feedback shift register (LFSR) to produce a keystream of period P ⩾ 2 n 2 , and linear complexity greater than half its period. In this article, we propose a new variant of the self-shrinking generator called the modified self-shrinking generator MSSG. This new generator is based on a primitive n-stage LFSR and uses an extended selection rule based on the XORed value of a pair of bits. We prove that the keystreams of the MSSG are balanced, and have period greater than or equal to 2 n 3 , linear complexity greater than half the period, and possess good statistical properties. We investigate the security of the generator against various powerful cryptanalytic attacks. We show that the MSSG is more secure than the SSG against most of these attacks. Moreover, experiments show that for odd values of n, 3 < n < 20 , the period of the keystreams generated by the MSSG attains its maximum value 2 n - 1 , and the linear complexity of these keystreams is very close to its upper bound. The NIST statistical test suite is applied to several thousands keystreams of the MSSG to demonstrate their good randomness properties. The obtained results show that keystreams of the MSSG have better randomness properties than those of the SSG.

Pseudorandom Bit Generation Using Coupled Congruential Generators

In this brief, we propose the generation of a pseudorandom bit sequence (PRBS) using a comparative linear congruential generator (CLCG) as follows. A bit ?1? is output if the first linear congruential generator (LCG) produces an output that is greater than the output of the second LCG, and a bit ?0? is output otherwise. Breaking this scheme would require one to obtain the seeds of the two independent generators given the bits of the output bit sequence. We prove that the problem of uniquely determining the seeds for the CLCG requires the following: 1) knowledge of at least log2 m 2 ( m being the LCG modulus) bits of the output sequence and 2) the solution of at least log2 m 2 inequalities, where each inequality (dictated by the output bit observed) is applied over positive integers. Computationally, we show that this task is exponential in n (where n = log2 m is the number of bits in m) with complexity O(22 n). The quality of the PRBS so obtained is assessed by performing a suite of statistical tests (National Institute of Standards and Technology (NIST) 800-22) recommended by NIST. We observe that a variant of our generator that uses two CLCGs (called dual CLCG) pass all the NIST pseudorandomness tests with a high degree of consistency.

키유도함수의 통계적 난수성 평가 방법

암호시스템에 사용되는 알고리즘의 기본적인 안전성 평가 항목은 난수성이다. 미국의 표준기술원 NIST는 차세대 암호알고리즘 AES를 선정하는 과정에서 블록암호의 난수성을 통계적으로 평가할 수 있는 패키지를 제안하였다. 이 패키지는 입출력 길이가 동일한 함수인 블록암호에 적합하도록 구성되어 있으므로 대부분 확장된 출력 길이를 갖는 키유도함수의 난수성 평가에 그대로 적용하는 것은 무리가 있다. 본 논문에서는 입력 길이보다 확장된 다중 블록을 출력하는 대표적인 암호 구성 요소인 키유도함수에 적합한 통계적 난수성 평가 방법으로 NIST의 방식을 개선한 것을 제안한다. 그리고 제안된 방법에 의하여 3GSM과 NIST에서 표준으로 권고하고 있는 키유도함수에 대한 통계적 난수성 평가결과를 제시한다. Randomness is a basic security evaluation item for the most cryptographic algorithms. NIST has proposed a statistical test suit for random number generators for cryptographic applications in the process of AES project. However the test suit of NIST is customized to block ciphers which have the same input and output lengths. It needs to revise NIST's test suit for key derivation functions which have multiple output blocks. In this paper we propose a revised method of NIST's statistical randomness test adequate to the most key derivation functions and some experimental results for key derivation functions of 3GSM and NIST.

On the pass rate of NIST statistical test suite for randomness

In this paper, the pass rate of the NIST SP800-22 statistical test suite for the ideally true random sequences is analyzed by the simulation of statistical tests, and derived by the theoretical analysis under the assumption that there are no correlation among tests. As examples of chaos based system, Vector Stream Cipher (VSC128S) and the encryption system using Arnold's cat map are tested. The test results are compared with the theoretical one for the true random sequences and validity of presented analysis is discussed.

SEARCH-BASED CHAOTIC PSEUDORANDOM BIT GENERATOR

This paper proposes the construction of a new chaotic pseudorandom bit generator, which forms the main building block of a chaotic stream cipher. The design of the algorithm is based on a single chaotic map whose numerical orbit indirectly contributes towards the generation of the keystream. The latter is produced from the numerical orbit by applying a technique that searches for iterates in specific intervals [a,b], for some real numbers a and b, and outputs 0 or 1 based on the iterate preceding the targeted iterate. The generator suggested here is built up from a quadratic map. We analyze the cycle length of the keystreams and investigate the resistance of the generator to well-known cryptanalytic attacks. Furthermore, the statistic characteristics of the keystreams are examined numerically using the NIST statistical test suite. The numerical and theoretical results demonstrate that the proposed technique results in generating keystreams possessing very good cryptographic properties and high level of security against existing cryptanalytic attacks. Empirical results show that the search technique leads to the generation of keystreams possessing good randomness properties when applied to any chaotic map whose orbits have good randomness properties such as the quadratic map, tent map and sawtooth map.

Analysis of Unpredictable Cryptographic Pseudo-random Number Generator based on Non-linear Dynamic Chaotic System

Most of pseudo-random number generators are unsuitable for cryptographic applications despite their statistical and correlation characteristics due to their backward and forward predictability. In this paper we presented an analysis of unpredictable cryptographic pseudo-random number generator based on non-linear dynamic chaotic system. We showed that we can get 48 bits from one float point and these bits generally passed NIST statistical test suite, therefore, we recommend to use this generator for cryptographic keys generation. Ill. 6, bibl. 6 (in English; summaries in English, Russian and Lithuanian).

Discrete asymptotic deterministic randomness for the generation of pseudorandom bits

The deterministic randomness not only can become a dominant approach in exploring the relationship between chaos and randomness, but also can be associated with some famous number theoretical concepts and open problems in number theory. Compared with chaotic sequences, asymptotic deterministic randomness sequences have the characteristic of multi-value correspondence, which makes those sequences unpredictable in short steps. In this Letter, we will propose the definition of the discrete asymptotic deterministic randomness, and then analyze the dynamical characteristics such as maximum-period and multi-value correspondence. Referring to the NIST800-22 statistical test suite, we will present and discuss two examples of PRBGs based on DADR, from the point of view of FPGA design and randomness quality.

Randomness quality of permuted pseudorandom binary sequences

This paper uses the DIEHARD statistical test suite to test the randomness quality of “permuted” versions of maximum length sequences generated by linear finite state machines (LFSM) such as cellular automata and linear feedback shift registers. Analysis shows that permuted sequences can be equivalently generated by using time-varying transformations derived from the original LFSM. Based on the above, we suggest the permuted transformation sequence scheme. Experimental results show that DIEHARD results are improved with respect to the original non-permuted sequences—up to seven more tests can be passed (total of 19 tests). Furthermore, a permutation vector is used to generate cyclically distinct permuted sequences and each sequence has a desirable maximum length period of 2n−1.

A Class of Maximum-Period Nonlinear Congruential Generators Derived From the R&amp;eacute;nyi Chaotic Map

In this paper, a family of nonlinear congruential generators (NLCGs) based on the digitized Reacutenyi map is considered for the definition of hardware-efficient pseudorandom number generators (PRNGs), and a theoretical framework for their study is presented. The authors investigate how the nonlinear structure of these systems eliminates some of the statistical regularities spoiling the randomness of sequences generated with linear techniques. In detail, in this paper, a necessary condition that the considered NLCGs must satisfy to have maximum period length is given, and a list of such maximum period PRNGs for period lengths up to 231-1 is provided. Referring to the NIST800-22 statistical test suite, two PRNG examples are presented and compared to well-known PRNGs based on linear recurrencies requiring a similar amount of resources for their implementation

Statistical complexity measure of pseudorandom bit generators

Pseudorandom number generators (PRNG) are extensively used in Monte Carlo simulations, gambling machines and cryptography as substitutes of ideal random number generators (RNG). Each application imposes different statistical requirements to PRNGs. As L’Ecuyer clearly states “the main goal for Monte Carlo methods is to reproduce the statistical properties on which these methods are based whereas for gambling machines and cryptology, observing the sequence of output values for some time should provide no practical advantage for predicting the forthcoming numbers better than by just guessing at random”. In accordance with different applications several statistical test suites have been developed to analyze the sequences generated by PRNGs. In a recent paper a new statistical complexity measure [Phys. Lett. A 311 (2003) 126] has been defined. Here we propose this measure, as a randomness quantifier of a PRNGs. The test is applied to three very well known and widely tested PRNGs available in the literature. All of them are based on mathematical algorithms. Another PRNGs based on Lorenz 3D chaotic dynamical system is also analyzed. PRNGs based on chaos may be considered as a model for physical noise sources and important new results are recently reported. All the design steps of this PRNG are described, and each stage increase the PRNG randomness using different strategies. It is shown that the MPR statistical complexity measure is capable to quantify this randomness improvement. The PRNG based on the chaotic 3D Lorenz dynamical system is also evaluated using traditional digital signal processing tools for comparison.

Application of multi-element statistical analysis for regional geochemical mapping in Central Japan

Some 434 stream sediment samples were collected in Central Japan for a nationwide geochemical mapping project. The resulting geochemical maps are compared with geological, mineral resource and land use maps. Spatial distribution patterns of elemental concentrations in stream sediments are determined mainly by surface geology. Elevated elemental concentrations of alkali elements, Be, Ga, Y, Cs, Ba, lanthanide (Ln), Tl, Th, and U are consistent with outcrop areas of granite, felsic volcanic rock, and accretionary complexes. High concentrations of MgO, Al 2O 3, P 2O 5, CaO, 3d transition metals, Zn, and Sr are present in sediments supplied from mafic volcanic rock, high pressure metamorphic rocks, and mafic-ultramafic rocks in accretionary complexes. A procedure is established and guidelines are set for a statistical test suite for geochemical mapping. Analysis of variance (ANOVA) and multiple comparison tests are effective for comparing means among the data subsets that are classified by parent lithological materials. Among the many procedures that have been proposed for multiple comparison tests, the Holm procedure was selected for this study. Multiple comparison statistically confirmed the correspondence of elemental abundance in stream sediments with surface geologies. However, visual interpretation of some elements is inconsistent with results of multiple comparison. According to the Holm procedure, the U content in stream sediments is affected not by granite, but by felsic volcanic rock. The Holm procedure clarifies that As, Sb, and Bi, that are not explained by the presence of mineral deposits, are enriched significantly in samples derived from accretionary complexes. Hydrothermal activity on the ocean floor might affect their levels of enrichment. Significant enrichment of Cu, Zn, Cd, Sn, Sb, Hg, and Pb observed in urban areas are also supported by the Holm procedure. The authors inferred that these sediment samples had been contaminated.

COMPARISON OF EXPOSURE ASSESSMENT METHODS FOR RISK ESTIMATION OF DISINFECTION BY-PRODUCTS

ISEE-243 Abstract: Summary statistics of quarterly water utility monitoring data in conjunction with data collected on water consumption and use are widely employed to calculate exposure in epidemiologic studies concerning disinfection by-products such as trihalomethanes (THM). However, this use of monitoring data can result in exposure misclassification due to spatial variation in THM concentrations within water distribution systems. Two methods, each designed to minimize misclassification error due to spatial variation, have been reported. The “weighting” metric assigns a weighting factor between 0.0 and 1.0 to frequency counts based on the degree of spatial variation (high to low) in each set of samples (sampling event) in a quarterly monitoring report. The “threshold” metric applies a suite of statistical tests to the same data in order to eliminate sampling events with high spatial variation, and thus restricts the study population used in the risk estimate. We compared these two methods in terms of classifying spatial variability in monitoring data, classifying exposure based on THM concentration, and calculating epidemiological risk estimates. We used utility (460 sampling events reported by 105 utilities over the period 1998–2002) and case/control data (200 participants matched to the THM data at date of conception) from Texas subjects in the National Birth Defects Prevention Study. We found good agreement between the two metrics in terms of categorizing and predicting sampling events as high or low in spatial variation. Across utilities with high and low THM concentrations, the weighting metric consistently assigned a weighting factor of < 0.89 when the threshold metric predicted low spatial variability. The proportions of cases and controls for the analyses of the threshold metric and the non-transformed data in the ’20 and <80 mg/L exposure categories were the same (56% and 44% respectively). These proportions were slightly different in the weighting metric analysis (<80 = 62%, ≤20 = 38%). Associated risk using the threshold metric (n=33) was higher (mean OR (CI) = 3.0(0.5,17.9)) than the risk calculated by the weighting metric (n=31, mean OR (CI)=1.9(0.3,10.8)) or by using non-transformed monitoring data (n=41, mean OR (CI)=1.8(0.4,2.1)). Our results indicated that using exposure metrics that adjust for spatial variation appear to improve detection of risk of birth defects in association with THM in water supplies. However, further validation by verifying predicted classification of degree of spatial variation for both metrics through field monitoring of DBP concentrations in utility water distribution systems is needed.

Biometric random number generators

Up to now biometric methods have been used in cryptography for authentication purposes. In this paper we propose to use biological data for generating sequences of random bits. We point out that this new approach could be particularly useful to generate seeds for pseudo-random number generators and so-called “key sessions”. Our method is very simple and is based on the observation that, for typical biometric readings, the last binary digits fluctuate “randomly”. We apply our method to two data sets, the first based on animal neurophysiological brain responses and the second on human galvanic skin response. For comparison we also test our approach on numerical samplings of the Ornstein–Uhlenbeck stochastic process. To verify the randomness of the sequences generated, we apply the standard suite of statistical tests (FIPS 140-2) recommended by the National Institute of Standard and Technology for studying the quality of the physical random number generators, especially those implemented in cryptographic modules. Additionally, to confirm the high cryptographic quality of the biometric generators, we also use the often recommended Maurer's universal test and the Lempel–Ziv complexity test, which estimate the entropy of the source. The results of all these verifications show that, after appropriate choice of encoding and experimental parameters, the sequences obtained exhibit excellent statistical properties, which opens the possibility of a new design technology for true random number generators. It remains a challenge to find appropriate biological phenomena characterized by easy accessibility, fast sampling rate, high accuracy of measurement and variability of sampling rate.