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Correlation Analysis of the Alternating Step Generator

机译:交流步进发生器的相关性分析

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The alternating step generator is a well-known keystream generator consisting of two stop/go clocked LFSRs, LFSR_1 and LFSR_2, whose clocks are controlled by another LFSR, LFSR_3, which is clocked regularly. A probabilistic analysis of this generator is conducted which shows that the posterior probabilites of individual bits of the first derivatives of the regularly clocked LFSR_1 and LFSR_2 sequences, when conditioned on a given segment of the first derivative of the keystream sequence, can be computed efficiently in a number of probabilistic models of interest. The expected values of these probabilities, for a random keystream sequence, are derived by an approximate theoretical analysis and are also verified by systematic computer experiments. It is pointed out that these posterior probabilities can be enhanced in a resynchronization scenario and thus used for a low-complexity fast correlation attack on the two LFSRs. More generally, it is argued that even without resynchronization these probabilities may be significantly different from one half for fast correlation attacks based on iterative decoding algorithms to be successful, although with incresead complexity. A related method for computing the posterior probabilities of individual bits of the LFSR_3 sequence, when conditioned on both the keystream sequence and the LFSR_1 and LFSR_2 sequences, is also developed. As these posterior probabilities are much more different from one half, they can be used for a low-complexity fast correlation attack on LFSR_3, provided that the initial states of LFSR_1 and LFSR_2 are previously reconstructed.
机译:交替步进生成器是众所周知的密钥流生成器,它由两个停止/开始计时的LFSR LFSR_1和LFSR_2组成,它们的时钟由另一个定期进行计时的LFSR LFSR_3控制。对此发生器进行了一次概率分析,结果表明,当以密钥流序列的一阶导数的给定段为条件时,规则计时的LFSR_1和LFSR_2序列的一阶导数的各个位的后验概率可以有效地计算出来。许多感兴趣的概率模型。对于随机密钥流序列,这些概率的期望值是通过近似理论分析得出的,并且还通过系统的计算机实验进行了验证。要指出的是,这些后验概率可以在重新同步的情况下得到增强,因此可以用于对两个LFSR的低复杂度快速相关攻击。更普遍地说,即使复杂性增加,即使没有重新同步,这些概率也可能与基于迭代解码算法的快速相关攻击成功的概率显着不同。还开发了一种相关的方法,当以密钥流序列以及LFSR_1和LFSR_2序列为条件时,可以计算LFSR_3序列的各个比特的后验概率。由于这些后验概率相差很大,因此可以将其用于LFSR_3的低复杂度快速相关攻击,前提是事先重建了LFSR_1和LFSR_2的初始状态。

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