伽罗瓦场GF(pn)中自收缩发生器的推广

Antoniya Tasheva, Zhaneta Tasheva, A. Milev
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引用次数: 15

摘要

Meier和Staffelbach提出的自收缩发生器(SSG)仅使用单个线性反馈移位寄存器就具有高效的硬件实现,适用于低成本和快速的流密码应用。本文推广了任意伽罗瓦场GF(pn)的SSG思想。提出的SSG的变体被称为p-ary广义自收缩发生器(pGSSG)。提出了一种将非二值自缩pGSSG序列转化为平衡二值序列的方法。我们证明了pGSSG的密钥流具有大周期和良好的统计特性。实验结果分析表明,pGSSG序列具有良好的随机性。我们研究了pGSSG的穷举搜索和熵攻击的复杂性。我们证明了pGSSG比SSG和修改后的SSG更安全。我们证明了所使用的pGSSG攻击的复杂性随着素数p的增加而增加。前面提到的属性使我们有理由说pGSSG满足流芯片的基本安全要求,并且可以作为现代流密码的一部分有用。
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Generalization of the Self-Shrinking Generator in the Galois Field GF(pn)
The proposed by Meier and Staffelbach Self-Shrinking Generator (SSG) which has efficient hardware implementation only with a single Linear Feedback Shift Register is suitable for low-cost and fast stream cipher applications. In this paper we generalize the idea of the SSG for arbitrary Galois Field GF(pn). The proposed variant of the SSG is called the p-ary Generalized Self-Shrinking Generator (pGSSG). We suggest a method for transformation of a non-binary self-shrunken pGSSG sequence into balanced binary sequence. We prove that the keystreams of the pGSSG have large period and good statistical properties. The analysis of the experimental results shows that the pGSSG sequences have good randomness properties. We examine the complexity of exhaustive search and entropy attacks of the pGSSG. We show that the pGSSG is more secure than SSG and Modified SSG against these attacks. We prove that the complexity of the used pGSSG attacks increases with increasing the prime p. Previously mentioned properties give the reason to say that the pGSSG satisfy the basic security requirements for a stream chipper and can be useful as a part of modern stream ciphers.
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