Boolean functions of binary Type-II and Type-III/II complementary array pairs

Cryptography and Communications Pub Date : 2024-02-24 DOI:10.1007/s12095-024-00701-6

Erzhong Xue, Zilong Wang, Jinjin Chai

引用次数: 0

Abstract

The sequence pairs of length \(2^{m}\) projected from Type-II and Type-III/II complementary array pairs of size \(2\times 2\times \cdots \times 2\) (m-times) form Type-II and Type-III complementary sequence pairs, respectively. An exhaustive search for binary Type-II and Type-III complementary sequence pairs of small lengths \(2^{m}\) (\(m=1,2,3,4\)) shows that they are all projected from the aforementioned complementary array pairs, whose algebraic normal forms satisfy specified expressions. It’s natural to ask whether the conclusion holds for all m. In this paper, we proved that these expressions of algebraic normal forms determine all the binary Type-II and Type-III/II complementary array pairs of size \(2\times 2\times \cdots \times 2\).

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二进制 Type-II 和 Type-III/II 互补阵列对的布尔函数

从大小为 \(2\times 2\times \cdots \times 2\) (m-times) 的 Type-II 和 Type-III/II 互补数组对投影出来的长度为 \(2^{m}\) 的序列对分别形成 Type-II 和 Type-III 互补序列对。对小长度 \(2^{m}\) （m=1,2,3,4）的二进制 Type-II 和 Type-III 互补序列对的穷举搜索表明，它们都是从上述互补数组对中投射出来的，其代数正常形式满足指定的表达式。在本文中，我们证明了这些代数正常形式的表达式决定了所有大小为 \(2\times 2\times \cdots \times 2\) 的二进制 Type-II 和 Type-III/II 互补数组对。

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

Cryptography and Communications

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