Long period pseudo random number sequence generator

A circuit for generating a sequence of pseudo random numbers, (A sub K). There is an exponentiator in GF(2 sup m) for the normal basis representation of elements in a finite field GF(2 sup m) each represented by m binary digits and having two inputs and an output from which the sequence (A sub K). Of pseudo random numbers is taken. One of the two inputs is connected to receive the outputs (E sub K) of maximal length shift register of n stages. There is a switch having a pair of inputs and an output. The switch outputs is connected to the other of the two inputs of the exponentiator. One of the switch inputs is connected for initially receiving a primitive element (A sub O) in GF(2 sup m). Finally, there is a delay circuit having an input and an output. The delay circuit output is connected to the other of the switch inputs and the delay circuit input is connected to the output of the exponentiator. Whereby after the exponentiator initially receives the primitive element (A sub O) in GF(2 sup m) through the switch, the switch can be switched to cause the exponentiator to receive as its input a delayed output A(K-1) from the exponentiator thereby generating (A sub K) continuously at the output of the exponentiator. The exponentiator in GF(2 sup m) is novel and comprises a cyclic-shift circuit; a Massey-Omura multiplier; and, a control logic circuit all operably connected together to perform the function U(sub i) = 92(sup i) (for n(sub i) = 1 or 1 (for n(subi) = 0)

Pseudo Random Coins Show More Heads Than Tails

Tossing a coin is the most elementary Monte Carlo experiment. In a computer the coin is replaced by a pseudo random number generator. It can be shown analytically and by exact enumerations that popular random number generators are not capable of imitating a fair coin: pseudo random coins show more heads than tails. This bias explains the empirically observed failure of some random number generators in random walk experiments. It can be traced down to the special role of the value zero in the algebra of finite fields.Comment: 10 pages, 12 figure

Testing for Randomness in Pseudo Random Number Generators Algorithms in a Cryptographic Application

The most effective cryptographic algorithm has more randomness in the numbers a generator generates, and the more secured it is to be used for protecting confidential data. Sometimes developers find it difficult to determine which Random Number Generators (RNGs) can provide a much secured Cryptographic System for secured enterprise application implementations. This research aims to find an effective Pseudo Random Number Generator algorithm among Fibonacci Random Numbers Generator Algorithms, Gaussian Random Numbers Generator Algorithm, Specific Range Random Numbers Generator Algorithms, and Secure Random numbers Generators, which are the most common Pseudo Random Numbers Generators Algorithms, that can be used to improve the security of Cryptographic software systems. The researchers employed Chi-Square test on the first 100 random numbers between 0 to 1000 generated using the above generators and it concluded that, Fibonacci Random Numbers Generator Algorithms can provide a more secured cryptographic application. Keywords Pseudo Random Number Generators, Randomness, Cryptography, Softwar

A Versatile Pseudo-Random Noise Generator

A detailed design is presented for a digital pseudo-random noise generator. The instrument is built with standard integrated circuits. It produces both binary noise (pseudo-random binary sequences) and white Gaussian noise of variable bandwidth. By setting front panel switches to match tabulated octal codes, one may select a vast number of independent noise programs

Pseudo-random number generator for the Sigma 5 computer

A technique is presented for developing a pseudo-random number generator based on the linear congruential form. The two numbers used for the generator are a prime number and a corresponding primitive root, where the prime is the largest prime number that can be accurately represented on a particular computer. The primitive root is selected by applying Marsaglia's lattice test. The technique presented was applied to write a random number program for the Sigma 5 computer. The new program, named S:RANDOM1, is judged to be superior to the older program named S:RANDOM. For applications requiring several independent random number generators, a table is included showing several acceptable primitive roots. The technique and programs described can be applied to any computer having word length different from that of the Sigma 5

A Horadam-based pseudo-random number generator

Uniformly distributed pseudo-random number generators are commonly used in certain numerical algorithms and simulations. In this article a random number generation algorithm based on the geometric properties of complex Horadam sequences was investigated. For certain parameters, the sequence exhibited uniformity in the distribution of arguments. This feature was exploited to design a pseudo-random number generator which was evaluated using Monte Carlo π estimations, and found to perform comparatively with commonly used generators like Multiplicative Lagged Fibonacci and the 'twister' Mersenne

Properties making a chaotic system a good Pseudo Random Number Generator

We discuss two properties making a deterministic algorithm suitable to generate a pseudo random sequence of numbers: high value of Kolmogorov-Sinai entropy and high-dimensionality. We propose the multi dimensional Anosov symplectic (cat) map as a Pseudo Random Number Generator. We show what chaotic features of this map are useful for generating Pseudo Random Numbers and investigate numerically which of them survive in the discrete version of the map. Testing and comparisons with other generators are performed.Comment: 10 pages, 3 figures, new version, title changed and minor correction

A horadam-based pseudo-random number generator

Uniformly distributed pseudo-random number generators are commonly used in certain numerical algorithms and simulations. In this article a random number generation algorithm based on the geometric properties of complex Horadam sequences was investigated. For certain parameters, the sequence exhibited uniformity in the distribution of arguments. This feature was exploited to design a pseudo-random number generator which was evaluated using Monte Carlo π estimations, and found to perform comparatively with commonly used generators like Multiplicative Lagged Fibonacci and the 'twister' Mersenne