基于Weierstrass函数的随机数发生器

研究了Weierstrass函数∑∞n=0ancos(bnπx)中a,b,x的取值对序列{xn}的随机性的影响;证明了b>1时能够产生具有不可预测性的优良随机序列{xn}.在此基础上设计了一个用于数据加密的随机数发生器.和其他的随机数发生器相比,在保持优良的随机性的前提下,该随机数发生器具有序列不可预测、较大的密钥空间、占用较小的存储空间、算法简单、实现方便等优点.在一定程度上加强了随机数发生器的安全性,符合一个较好的随机数发生器的要求.

A Random Number Generator Based on Weierstrass Function

The effects of what values the a, b, x take in the Weierstrass function ∑aⁱ cos(bⁱπx) on the randomness of the sequence {xn} are studied. It is proved that it will generate an unpredictable good random sequence {xn} when b>1. Then, a random number generator is designed for data encryption. Compared with other generators, it has several merits such as the unpredictability of the sequence, bigger secret key space, smaller storage space, simpler algorithm and easier to implement in addition to its long period, quick running speed, high compatibility and reproducibility of good randomness. The security of random number generator is thus enhanced, to a certain extent, thus meeting the requirements of a high-performance generator.