Deciding Irreducibility/Indecomposability of Feedback Shift Registers Is NP-Hard

IF 1.3 4区计算机科学 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS IET Information Security Pub Date : 2024-03-07 DOI:10.1049/2024/3219604

Lin Wang

引用次数: 0

Abstract

Feedback shift registers (FSRs) are used as a fundamental component in electronics and confidential communication. A FSR f is said to be reducible if all the output sequences of another FSR g can also be generated by f and the FSR g costs less memory than f. A FSR is said to be decomposable if it has the same set of output sequences as a cascade connection of two FSRs. Two polynomial-time computable transformations from Boolean circuits to FSRs are proposed such that the output FSR of the first (resp. second) transformation is irreducible (resp. indecomposable) if and only if the input Boolean circuit is satisfiable. Through the two transformations, it is proved that deciding irreducibility (indecomposability) of FSRs is NP-hard. Additionally, FSRs are constructed to show that there exist infinitely many irreducible (resp. indecomposable) FSRs which are decomposable (resp. reducible).

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决定反馈移位寄存器的不可重复性/不可分性是 NP-困难的

反馈移位寄存器（FSR）是电子和保密通信中的基本组件。如果另一个 FSR g 的所有输出序列也能由 f 生成，且 FSR g 的内存消耗低于 f，则称 FSR f 是可还原的。本文提出了两种从布尔电路到 FSR 的多项式时间可计算变换，当且仅当输入布尔电路是可满足的时，第一种（或第二种）变换的输出 FSR 是不可还原的（或不可分解的）。通过这两种变换，证明了判定 FSR 的不可还原性（不可分解性）是 NP-困难的。此外，通过构建 FSR 还可以证明，存在无限多的不可还原（或不可分解）的 FSR，这些 FSR 都是可分解（或可还原）的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

IET Information Security 工程技术-计算机：理论方法

CiteScore

3.80

自引率

7.10%

发文量

审稿时长

8.6 months

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