• 计算机安全 •

### 对称布尔函数的算术相关函数

1. 1.
2. 西安邮电大学 通信与信息工程学院，西安 710121
• 收稿日期:2013-07-29 修回日期:2013-10-14 出版日期:2014-02-01 发布日期:2014-03-01
• 通讯作者: 赵庆兰
• 作者简介:赵庆兰（1981-），女，山东曹县人，讲师，博士研究生，主要研究方向：密码学、信息安全；郑东（1964-），男，山西翼城人，教授，博士生导师，博士，主要研究方向：云计算安全、密码学；董晓丽(1980-)，女，山西阳曲人，讲师，博士，主要研究方向：密码算法。
• 基金资助:
陕西省自然科学基础研究计划重点项目;陕西省自然科学基础研究计划重点项目;陕西省教育厅科学研究计划项目;西安邮电大学校青年基金资助项目

### Arithmetic correlations of symmetric Boolean function

ZHAO Qinglan1,2,ZHEN Dong1,2,DONG Xiaoli1,2

1. 1. National Engineering Laboratory for Wireless Security, Xi'an Shaanxi 710121，China
2. School of Telecommunication and Information Engineering, Xi'an University of Posts and Telecommunications, Xi'an Shaanxi 710121,China
• Received:2013-07-29 Revised:2013-10-14 Online:2014-02-01 Published:2014-03-01
• Contact: ZHAO Qinglan

Abstract: The arithmetic correlation function is a new method for studying the cryptographic properties of Boolean functions. Based on the basic definitions of addition and multiplication of multi-2-adic integer, the study constructed a new algebraic ring and realized the arithmetic or “with-carry” analogs of classic correlation functions. In this paper the definition of arithmetic autocorrelation function was introduced. The arithmetic correlation value of symmetric Boolean functions was studied. The results show that the arithmetic autocorrelation function of symmetric Boolean functions is a real symmetric function with at most n1 values.