Relationship Between the Algebraic Immunity of Multi-Output Boolean Functions and Boolean Functions

WANG Qiu-yan; JIN Chen-hui

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Relationship Between the Algebraic Immunity of Multi-Output Boolean Functions and Boolean Functions

更新时间：2025-07-16

- Relationship Between the Algebraic Immunity of Multi-Output Boolean Functions and Boolean Functions
- Acta Electronica Sinica Vol. 39, Issue 1, Pages: 124-127(2011)
- 作者机构：
  
  信息工程大学电子技术学院,河南,郑州,450004
- 作者简介：
- 基金信息：
- DOI：
  CLC： TN918.1
- Published：2011
- 稿件说明：
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WANG Qiu-yan, JIN Chen-hui. Relationship Between the Algebraic Immunity of Multi-Output Boolean Functions and Boolean Functions[J]. Acta Electronica Sinica, 2011, 39(1): 124-127.
DOI：

WANG Qiu-yan, JIN Chen-hui. Relationship Between the Algebraic Immunity of Multi-Output Boolean Functions and Boolean Functions[J]. Acta Electronica Sinica, 2011, 39(1): 124-127. DOI：

摘要

本文给出了多输出布尔函数状态函数集合的代数结构

证明了多输出布尔函数的代数免疫阶等于某布尔函数的代数免疫阶

且该布尔函数是多输出函数的分量函数的一个非零非线性组合.接着证明了该组合的代数免疫阶是所有非零非线性组合中最小的

从而得出多输出布尔函数的代数免疫阶等于其所有非零非线性组合代数免疫阶的最小值.

Abstract

This paper presents the algebraic structure of the conditional equations set for multi-output Boolean functions

proves that the algebraic immunity of multi-output Boolean functions is equal to that of a certain Boolean function

which is a combination of the component functions for multi-output Boolean functions

and among all combinations

this one has the minimum algebraic immunity.Hence

it can be concluded that the algebraic immunity of multi-output Boolean functions is equal to the minimum of algebraic immunities of all combinations.

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