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Our results show that the rate of correlation among the random variables of those output sequences are low although they are not independent; in addition, the output sequences of those combined generators are homogeneous Markov chains which are strictly stationary processes with ergodicity; the output sequences of those combined generators are also proved to summit to the strong law of large numbers and the central limit theorem; finally the computation formula of the rate of the accordance between the output sequences and input sequences of those combined generators is given.

我们的研究结论表明:虽然这些序列中随机变量之间不具有相互独立性,但它们的相关程度却比较低;证明了"停走"生成器,KM_1M_2型组合生成器和加法型组合生成器的概率模型输出序列都是强平稳的和遍历的齐次马氏链;讨论了这些序列的概率极限性质,证明了它们均服从强大数定律和中心极限定理;还分别给出了各类生成器的输出序列与输入序列之间的符合率的计算公式。

Secondly, the properties of output sequences of stop-and-go clocked combiners are discussed. It is proved that the output sequences are stationary and obey strong law of large numbers and central limit theorem. Using the probabilistic model properly built, we analyze the rate of coincidence between the output sequences of two kinds of generators with basic operations and corresponding LFSRs sequences. All the computational formulae are derived. A recursive algorithm for efficiently computing the poster probability of partial input strings and corresponding joint probability is introduced. Moreover, divide-and-conquer attacks on this kind of generators which reconstruct the initial states of the input stop-and-go generators individually are proposed.

其次,分析了一般钟控停走组合生成器输出序列的概率分布性质,证明了生成器的输出序列是严平稳的,且服从强大数定律和中心极限定理;考察了钟控加法型组合生成器和钟控乘法型组合生成器的输出序列和相应的常规钟控下线性移位寄存器序列之间的符合率,给出了符合率的具体计算公式;给出了组合器输出序列段和输入序列段之间的联合分布以及部分输入序列段的后验概率的有效递归算法,进一步提出了利用后验概率对钟控组合生成器进行分别征服相关攻击的方法。

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