This paper has used linear

congruential generator for generating initial pad and then genetic algorithm is used to improve the randomness of the initial pad.

The source noise can be obtained algorithmically using, for example, a

congruential generator, or physically, using a semiconductor noise generator.

As it is usually implemented, the algorithm is known as a Prime Modulus Multiplicative Linear

Congruential Generator. It is better known as a Lehmer generator.

As a last resort, Ferrenberg substituted different random-number generators and, to his surprise, found that he came much closer to the correct answer by using a linear

congruential generator, which has known defects.

--param selects the appropriate parameters (e.g., the multiplier for a Linear

Congruential Generator or the lag for a Lagged Fibonacci Generator).

* The

congruential generator [x.sub.n] = 16807[x.sub.n]-1 mod [2.sup.31] - 1 is a good generator, but not a great generator.

"A good

congruential generator could be used to run the casinos in Las Vegas and Atlantic City and all the state lotteries with no one the wiser."

We have used a linear

congruential generator fish by Fishman and Moore [1986], an explicit inversive

congruential generator [Eichenauer-Herrmann 1993], and a twisted GFSR generator (tt800 by Matsumoto and Kurita [1994]); at last the infamous randu (again an LCG) as an example of a generator with bad lattice structure (see Park and Miller [1988]).

Equation (1) defines a linear

congruential generator (LCG) in matrix form.

Wu [1997] proposed a clever-looking way to select the parameters and implement a linear

congruential generator (LCG): take a Mersenne prime modulus m, i.e., a prime of the form m = [2.sup.e] - 1 (see Knuth [1997] for more on Mersenne primes), and a multiplier of the form

The BMT uses sine and cosine functions--periodic functions that, when used in conjunction with a linear

congruential generator (LCG) such as the Lehmer generator, produces statistically correlated "random" numbers.

Although R250 passed a number of statistical tests, a recent experience [Selke 1993] showed that R250 gives wrong results for a clustered Monte Carlo simulation, while the multiplicative

congruential generator