The Generation And Application Of Some Random Number Generators

The random number generator is the basic tool of random simulation.A good generator is favor of the simalate work, contrarily a bad generator will break down the work.At present the abroadly used method in computer simulation is maths mea-ture.It uses iterative formula produces random number.This paper first introduce the linear congruential generator, the Tausworthe generator and some ordinary random number generator.These methods have been applied since those were invented.We point out the drawbacks in classical random number generators, and then introduce theory on combined random number generator.Combined random number generator is a random number generator that made up of several generators.For insrance, a linear combination of several linear congruential generators.Based on the above theory and spectral test method, we give two combined random number generators.From the comprehensive test of localran-dommness, these, combined random number generator are with high quality.One of them is the combined generator based on several linear congruential generators[9].It proves that the combined generator is still a inear congruential generator provided that the moduli M₁,…, M_J of all these linear congruential generators would be pair-wise relatively prime integers.It also proves that the period of combined generator equals the least common multiple of periods T₁,…,T_J of all these linear congruential generators provided that the highest power of every prime factor p_i in canonical factorizations of T,…,T_J would not appear more than one time and (M_j,δ_j)=1 for j=1,…, J.The other one is based on the parabola way[3].When the random numeral array produced in a parabola way is disordered by random numerals produced by Linear Congruence Generator , the new random numeral array obtained is of more superior statistical characteristics , and it s period can be regarded as infinitely long and is of practical value.A special property of prime numbers was addressed and used for generating quasi-random numbers[4].First it was proved that let M be a selected prime number, all of which constitutes a subset of prime numbers, and Z be a whole number, 0 < Z < M, then Z/M yields a pure circulating decimal with a repetend of (M—1).By defining this special property of the prime numbers , a theorem was proved which provides a congruentialmethod for generating number sequence {z_i} with a period of (M - 1) and z_i∈[1, m -1] and z_i; being uniformly dist ributed within [1, M - 1] in one period. Finally , based on the above analysis , a congruential method for generating quasi- random numbers was proposed[5].Based on a special property of prime numbers and it s applications reported a prior , an improved method was addressed for generating longer period pseudo-random numbers. Examples and congruential schemes of the new method were provided to illust rate it s applications. Statistic result s show that the new method has advantages of satisfactory statistic properties over the method previously reported and the multiplicative or mixed congruential methods , particularly in view of it s long period of M(M—1), where M is a super prime number.In the last the paper discusses three applied instances about randomizer[6].The first is that we can use random number to explain the integral value in a area.The second is random number used in the simulate training equipment.The last is random number used in the secrecy transmission.We introduce the theory and history of code. Then we discuss an arithmetic of encrypt-RSA, introduce the character and theory of RSA.