Multiplicative Linear Congruential Generator Research Articles

Classical Hybrid Technique – Substitution and Transposition Techniques

The most important issue for every organization is nothing but security. This paper deals with the confidentiality of electronic data which is transmitted over the internet. To ensure security we are cryptography. “Cryptography” is the process of converting readable format of text to unreadable format of text. This is mainly used for secured communication. Many ciphers have been developed to provide security. Out of these techniques we considered five cipher techniques those are “Caesar Cipher, Mono alphabetic Cipher, Poly alphabetic Cipher, Row Transposition Technique, and Rail fence Techniques”. The main objective of this proposed system is to combine the functionality of these five techniques to overcome the disadvantages of these techniques and to form a new hybrid technique named as “Classical Hybrid Encryption Substitution and Transposition Techniques” which can provide a good security when compared to techniques. This method uses two stages of encryption. In the first stage Substitution techniques – Mono alphabetic, Caesar cipher, poly alphabetic cipher are used to generate partial cipher text. The key for Caesar cipher and poly alphabetic technique is generated randomly by using Multiplicative linear congruential generator (Random number generation technique). In the second stage of Encryption Technique Transposition methods – Row Transposition and Rail fence Techniques are used to generate final cipher text. This algorithm provides 91! Of key space and in addition of that this encryption technique is multistage with each stage uses different key. Through this technique we will achieve good security against Brute-Force Attack and Cryptanalysis.

Image Encryption Using Chaotic Map and Prime modulo Multiplicative LinearCongruential Generator

The chaos based cryptographic algorithms have suggested some new and efficient ways to develop secure image encryption techniques because of its exceptionally desirable properties of sensitivity to initial condition and parameters of chaotic map. In this study an image encryption algorithm is presented, in which chaos based encryption technique and prime modulo multiplicative linear Congruential generator (PMMLCG) has been used to improve the quality of image encryption and to achieve the goal of pixel scrambling. The proposed algorithm generates random numbers, which are used in row shuffling, column shuffling and pixel scrambling which results in encryption technique highly resistive to cryptanalytic attack. Results and effectiveness is measured in qualitative and quantitative metrics which shows that this encryption algorithm is securefor encryption of images.

Pseudorandom Number Generation in the Context of a 3D Simulation Model for Tissue Growth

In this paper, we consider our choice of a pseudorandom number generator (PRNG) in the context of running a simulation model for the growth of 3D tissues. This PRNG is the multiplicative linear congruential generator (MLCG) with carefully chosen parameters. We base our selection of this generator on three criteria. They are periodicity, randomness quality, and ease of implementation. In these regards, we review some of the pertinent theoretical properties of the employed MLCG and describe techniques used to obtain such sequences serially. Our investigation indicates that the MLCG, with properly selected parameters, can be a good, portable, user-specified, and user-controlled generator with acceptable quality. During the simulation of tissue growth, our various experiments have also shown that the ratio of the total number of random numbers consumed till confluence to the total number of computational sites in the cellular array never exceeds a certain number. This number can be used as a predictor for the period of a PRNG needed to run a particular experiment to simulate tissue growth and to estimate when a longer period may be required in order to deal with very large data sets.

A package of Linux scripts for the parallelization of Monte Carlo simulations

Despite the fact that fast computers are nowadays available at low cost, there are many situations where obtaining a reasonably low statistical uncertainty in a Monte Carlo (MC) simulation involves a prohibitively large amount of time. This limitation can be overcome by having recourse to parallel computing. Most tools designed to facilitate this approach require modification of the source code and the installation of additional software, which may be inconvenient for some users. We present a set of tools, named clonEasy, that implement a parallelization scheme of a MC simulation that is free from these drawbacks. In clonEasy, which is designed to run under Linux, a set of “clone” CPUs is governed by a “master” computer by taking advantage of the capabilities of the Secure Shell (ssh) protocol. Any Linux computer on the Internet that can be ssh-accessed by the user can be used as a clone. A key ingredient for the parallel calculation to be reliable is the availability of an independent string of random numbers for each CPU. Many generators—such as RANLUX, RANECU or the Mersenne Twister—can readily produce these strings by initializing them appropriately and, hence, they are suitable to be used with clonEasy. This work was primarily motivated by the need to find a straightforward way to parallelize PENELOPE, a code for MC simulation of radiation transport that (in its current 2005 version) employs the generator RANECU, which uses a combination of two multiplicative linear congruential generators (MLCGs). Thus, this paper is focused on this class of generators and, in particular, we briefly present an extension of RANECU that increases its period up to ∼ 5 × 10 27 and we introduce seedsMLCG, a tool that provides the information necessary to initialize disjoint sequences of an MLCG to feed different CPUs. This program, in combination with clonEasy, allows to run PENELOPE in parallel easily, without requiring specific libraries or significant alterations of the sequential code. Program summary 1

Tables of linear congruential generators of different sizes and good lattice structure

We provide sets of parameters for multiplicative linear congruential generators (MLCGs) of different sizes and good performance with respect to the spectral test. For ℓ = 8 , 9 , … , 64 , 127 , 128 \ell = 8, 9, \dots , 64, 127, 128 , we take as a modulus m m the largest prime smaller than 2 ℓ 2^\ell , and provide a list of multipliers a a such that the MLCG with modulus m m and multiplier a a has a good lattice structure in dimensions 2 to 32. We provide similar lists for power-of-two moduli m = 2 ℓ m = 2^{\ell } , for multiplicative and non-multiplicative LCGs.

An efficient algorithm for testing the quality of the output of random number generators

This paper presents an efficient method and a computer program utilizing Walsh functions to test the quality of the output of a random number generator. The computer program is written in ZBasic and consists of six segments: (1) PMMLCG RANDOM NUMBER GENERATOR FUNCTION — This segment defines the portable Prime Modulus Multiplicative Linear Congruential Generator that is used as part of the Composite Sherif Dear (CSD) Random Number Generator, which is under study and testing in this paper; (2) INITIAL VARIABLE INPUT/HEADER OUTPUT — This segment requests user input for the experiment and prepares the output file with header information; (3) CSD RANDOM NUMBER GENERATOR SAMPLES — This segment generates multiple samples of the CSD Random Number Generator each with the desired sample size. The generated values are offset by 0·5; (4) DETERMINE THE WALSH TRANSFORM — This segment determines the Walsh Transform using a Manz Sequency Ordered In-Place Algorithm for the given sample; (5) DETERMINE THE KOLMOGOROV-SMIRNOV SAMPLE STATISTIC — This segment computes the Kolmogorov-Smirnov sample statistic on the scaled Walsh Transform; (6) SAMPLING COMPLETE-SUMMARIZE RESULTS — This segment summarizes the results for all samples and places the results into an output file. The Walsh functions based test shows that the output of the (CDS) random number generator satisfies the criteria of good random number generators.

The microcomputer performance of uniform variate random number generators expressed in FORTRAN

The microcomputer performance of random number generators is an important component of uncertainty analysis in environmental modeling. The results of a performance study of 110 uniform variate pseudo-random number generators expressed in FORTRAN are presented. The algorithms tested include multiplicative, mixed, additive and quadratic congruential generators plus example combined and generalized feedback shift register generators. Results are presented for generator speed, period, and 17 statistical measures of number randomness quality. These results indicate that, based on both speed and number quality, the multiplicative linear congruential generator can yield superior performance. Specific moduli and multipliers are recommended for this generator. For relatively low period generators, explicit use of the integer modulus function provides superior performance. When high period generators are implemented, they should be based on the Schrage (1979) or Bongiovanni (1987) computational procedure for accomplishing the modulus operation with arithmetic that avoids explicit use of the modulus function.

Efficient and portable combined random number generators

In this paper we present an efficient way to combine two or more Multiplicative Linear Congruential Generators (MLCGs) and propose several new generators. The individual MLCGs, making up the proposed combined generators, satisfy stringent theoretical criteria for the quality of the sequence they produce (based on the Spectral Test) and are easy to implement in a portable way. The proposed simple combination method is new and produces a generator whose period is the least common multiple of the individual periods. Each proposed generator has been submitted to a comprehensive battery of statistical tests. We also describe portable implementations, using 16-bit or 32-bit integer arithmetic. The proposed generators have most of the beneficial properties of MLCGs. For example, each generator can be split into many independent generators and it is easy to skip a long subsequence of numbers without doing the work of generating them all.