Hurst's Rescaled Range Statistical Analysis for Pseudorandom Number Generators used in Physical Simulations

The rescaled range statistical analysis (R/S) is proposed as a new method to detect correlations in pseudorandom number generators used in Monte Carlo simulations. In an extensive test it is demonstrated that the RS analysis provides a very sensitive method to reveal hidden long run and short run correlations. Several widely used and also some recently proposed pseudorandom number generators are subjected to this test. In many generators correlations are detected and quantified.Comment: 12 pages, 12 figures, 6 tables. Replaces previous version to correct citation [19

A Search for Good Pseudo-random Number Generators : Survey and Empirical Studies

In today's world, several applications demand numbers which appear random but are generated by a background algorithm; that is, pseudo-random numbers. Since late $19^{th}$ century, researchers have been working on pseudo-random number generators (PRNGs). Several PRNGs continue to develop, each one demanding to be better than the previous ones. In this scenario, this paper targets to verify the claim of so-called good generators and rank the existing generators based on strong empirical tests in same platforms. To do this, the genre of PRNGs developed so far has been explored and classified into three groups -- linear congruential generator based, linear feedback shift register based and cellular automata based. From each group, well-known generators have been chosen for empirical testing. Two types of empirical testing has been done on each PRNG -- blind statistical tests with Diehard battery of tests, TestU01 library and NIST statistical test-suite and graphical tests (lattice test and space-time diagram test). Finally, the selected $29$ PRNGs are divided into $24$ groups and are ranked according to their overall performance in all empirical tests

Acceleration techniques for dependability simulation

As computer systems increase in complexity, the need to project system performance from the earliest design and development stages increases. We have to employ simulation for detailed dependability studies of large systems. However, as the complexity of the simulation model increases, the time required to obtain statistically significant results also increases. This paper discusses an approach that is application independent and can be readily applied to any process-based simulation model. Topics include background on classical discrete event simulation and techniques for random variate generation and statistics gathering to support simulation

Analysis and improvement of S-Box in Rijndael- AES algorithm

The internet has become a part of everyday life and is used as a communication tool, a way to bank, invest, shop and an educational and entertainment medium. As the importance and popularity of the internet has grown over the years, so has the number of threats from hackers on the internet which has necessitated the need for the encryption of confidential data. Various methods of data encryption have been used over time, with developments being made to improve these techniques as hackers develop improved ways of attacking the algorithms used for encryption. This process of continued improvement of cryptographic security brought about the development and acceptance of the Advanced Encryption Standard (AES), which is a National Institute of Standards and Technology specification for the encryption of electronic data including financial, telecommunications, and government data. The Rijndael algorithm was selected as the encryption algorithm for AES in October 2001 and is currently used by government agencies and the private sector to secure sensitive unclassified information. Research has shown that Rijndael is susceptible to differential/ linear cryptanalysis for 7 and 8-round Rijndael, saturation attacks, algebraic attacks and side channel attacks on reduced versions of Rijndael, which could pave the way for a full-blown attack on the Rijndael algorithm in the future. This research investigates the weaknesses present in the Rijndael algorithm using various custom-made testing tools and then using the results of this investigation to improve the security of the algorithm. The improvement is provided in the form a technique of generating highly non-linear output using a non-linear random number generator which uses the recursive inverse congruential method. The research will comprise of three phases; literature review, analysis of the Rijndael algorithm using custom-made tools and development of an improvement whose performance will be evaluated in comparison to the current algorithm

An optimization technique on pseudorandom generators based on chaotic iterations

International audienceInternet communication systems involving cryptography and data hiding often require billions of random numbers. In addition to the speed of the algorithm, the quality of the pseudo-random number generator and the ease of its implementation are common practical aspects. In this work we will discuss how to improve the quality of random numbers independently from their generation algorithm. We propose an additional implementation technique in order to take advantage of some chaotic properties. The statistical quality of our solution stems from some well-defined discrete chaotic iterations that satisfy the reputed Devaney's definition of chaos, namely the chaotic iterations technique. Pursuing recent researches published in the previous International Conference on Evolving Internet (Internet 09, 10, and 11), three methods to build pseudorandom generators by using chaotic iterations are recalled. Using standard criteria named NIST and DieHARD (some famous batteries of tests), we will show that the proposed technique can improve the statistical properties of a large variety of defective pseudorandom generators, and that the issues raised by statistical tests decrease when the power of chaotic iterations increase

Family of PRGs based on Collections of Arithmetic Progressions

We consider the mathematical object: \textit{collection of arithmetic progressions} with elements satisfying the property: \textit{$j^{th}$ terms of $i^{th}$ and $(i+1)^{th}$ progressions of the collection are multiplicative inverses of each other modulo the $(j+1)^{th}$ term of $i^{th}$ progression}. Under a \textit{certain} condition on the common differences of the progressions, such a collection is {\em uniquely} generated from a pair of co-prime seed integers. The object is closely connected to the standard Euclidean gcd algorithm. In this work, we present one application of this object to a novel construction of a new family of pseudo random number generators (PRG) or symmetric key ciphers. We present an authenticated encryption scheme which is another application of the defined object. In this paper, we pay our attention to a basic symmetric key method of the new family. The security of the method is based on a well-defined hard problem. Interestingly, a special case of the hard problem (defined as Problem A) is shown to be computationally equivalent to the problem of factoring integers. The work leaves some open issues, which are being addressed in our ongoing work

Acceleration Techniques for Dependability Simulation

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryOffice of Naval ResearchComp. Sci. Corp.National Aeronautics and Space AdministrationU of I OnlyRestricted to UIUC communit

Advancing the iid Test Based on Integration across the Correlation Integral: Ranges, Competition, and Power

This paper builds on Kočenda (2001) and extends it in two ways. First, two new intervals of the proximity parameter ε (over which the correlation integral is calculated) are specified. For these ε- ranges new critical values for various lengths of the data sets are introduced and through Monte Carlo studies it is shown that within new ε-ranges the test is even more powerful than within the original ε-range. A sensitivity analysis of the critical values with respect to ε-range choice is also given. Second, a comparison with existing results of the controlled competition of Barnett et al. (1997) as well as broad power tests on various nonlinear and chaotic data are provided. The results of the comparison strongly favor our robust procedure and confirm the ability of the test in finding nonlinear dependencies. An empirical comparison of the new ε-ranges with the original one shows that the test within the new ε-ranges is able to detect hidden patterns with much higher precision. Finally, new user-friendly and fast software is introduced.chaos, nonlinear dynamics, correlation integral, Monte Carlo, single-blind competition, power tests, high-frequency economic and financial data