The estimates of trigonometric sums and new bounds on a mean value, a sequence and a cryptographic function

被引：1

作者：

Tong, Yan ^{[1
]}

Zeng, Xiangyong ^{[2
]}

Zhang, Shasha ^{[2
]}

Xu, Shiwei ^{[3
]}

Ren, Zhengwei ^{[4
,5
]}

机构：

[1] Huazhong Agr Univ, Coll Sci, Wuhan 430070, Peoples R China

[2] Hubei Univ, Fac Math & Stat, Hubei Key Lab Appl Math, Wuhan 430062, Peoples R China

[3] Huazhong Agr Univ, Coll Informat, Wuhan 430070, Peoples R China

[4] Wuhan Univ Sci & Technol, Coll Comp Sci & Technol, Wuhan 430065, Peoples R China

[5] Hubei Prov Key Lab Intelligent Informat Proc & Re, Wuhan 430065, Peoples R China

来源：

DESIGNS CODES AND CRYPTOGRAPHY | 2023年 / 91卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Trigonometric sum; Arithmetic mean value; Linear feedback shift register; Carlet-Feng (vectorial )Boolean function; Nonlinearity; VECTORIAL BOOLEAN FUNCTIONS; OPTIMAL ALGEBRAIC IMMUNITY; INFINITE CLASS; CONSTRUCTIONS; NONLINEARITY; INEQUALITY; THEOREMS; NUMBER;

D O I：

10.1007/s10623-022-01140-1

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this paper, we discuss the properties of the derivative of a special function, and propose a general approach to estimating a class of trigonometric sums based on the derivative of the special function. Then we apply the approach to three trigonometric sums and get three new estimates. Using the estimate of the first trigonometric sum, we deduce new upper and lower bounds of the arithmetic mean value for a trigonometric sum of Vinogradov. Using the estimate of the second trigonometric sum, we derive a new upper bound on the imbalance properties of Linear Feedback Shift Register subsequences. We also deduce a new lower bound on the nonlinearity of the Carlet-Feng vectorial Boolean function with the estimate of the third trigonometric sum.

引用

页码：921 / 949

页数：29

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