S004114-信息安全数学基础

发布者:沈如达发布时间:2018-04-23浏览次数:60

研究生课程开设申请表

 开课院(系、所):  信息科学与工程学院

 课程申请开设类型: 新开     重开□     更名□请在内打勾,下同

课程

名称

中文

信息安全数学基础

英文

Mathematical Foundations of Information Security

待分配课程编号


课程适用学位级别

博士


硕士

总学时

54

课内学时

54

学分

3

实践环节

0

用机小时

0

课程类别

公共基础     专业基础     专业必修     专业选修

开课院()

信息科学与工程学院

开课学期

秋季

考核方式

A.笔试(开卷   闭卷)      B. 口试    

C.笔试与口试结合                 D. □其他

课程负责人

教师

姓名

康维

职称

上岗副研究员

e-mail

wkang79@gmail.com

网页地址


授课语言

汉语

课件地址


适用学科范围

二级学科(信息安全)

所属一级学科名称

信息与通信工程

实验(案例)个数


先修课程


教学用书

教材名称

教材编者

出版社

出版年月

版次

主要教材

信息安全数学基础

陈恭亮

清华大学出版社

20046

1

主要参考书

信息安全数学基础

覃中平等

清华大学出版社

20068

1

信息安全数学基础

贾春福

南开大学出版社

20068

1

信息安全数学基础

李继国等

武汉大学出版社

20069

1

信息安全数学基础

谢敏

西安电子科技大学出版社

20068

1

代数

Michael Artin

机械工业出版社

20043

1

初等数论及其应用

Kenneth H. Rosen

机械工业出版社

20053

5


一、课程介绍(含教学目标、教学要求等)300字以内)

本课程系统地介绍信息安全所需要的基础数论与抽象代数知识。 包括数论中的同余,二次剩余,原根与指数,以及代数中的群,环,域,以及有限域的知识。通过本课程的学习,为研究生在信息安全领域中进一步学习与研究奠定必要的数学基础。


二、教学大纲(含章节目录):(可附页)

  1. 整除

    1. 整数的整除

    2. 欧几里德除法

    3. 最大公约数

    4. 算数基本定理

  2. 同余

    1. 同余基本性质

    2. 剩余类与剩余系

    3. 欧拉定理与费马小定理

    4. 中国剩余定理

  3. 二次剩余

    1. Legendre 符号

    2. Jacobi 符号

    3. 二次同余方程

  4. 原根与指数

    1. 原根

    2. 指数

    1. 子群与配集

    2. 商群

    3. 同构与同态

    1. 理想与商环

    2. 多项式环

    1. 有限域

    2. 最小多项式与本原多项式

    3. 有限域的结构,表示与计算


三、教学周历

 周次

 教学内容

 教学方式

1

整数的整除,欧几里德除法

 讲课

2

最大公约数与最小公倍数,算数基本定理

 讲课

3

同余基本性质,剩余类与剩余系

 讲课

4

欧拉定理与费马小定理

 讲课

5

中国剩余定理

 讲课

6

Legendre 符号

 讲课

7

Jacobi 符号

 讲课

8

二次同余方程

 讲课

9

原根,指数

 讲课

10

 讲课

11

子群与配集

 讲课

12

商群,同构与同态

 讲课

13

环,理想与商环

 讲课

14

多项式环

 讲课

15

域,有限域

 讲课

16

最小多项式与本原多项式

 讲课

17

有限域的结构,表示与计算

 讲课

18


 考试

四、主讲教师简介:

康维:19798月出生,男,博士,副研究员。2001年本科毕业于北京邮电大学电子工程系,2003年获得加拿大蒙特利尔麦吉尔大学电机与计算机工程系硕士,2008年获得美国马里兰大学电机与计算机工程系博士。20091月至今于东南大学信息科学与工程学院信息安全研究中心任副研究员。2008-2009年任Chinacom会议技术委员会(Technical Program Committee)委员。任IEEE Transaction on Information Theory, IEEE Transaction on Communications, IEEE Transaction on Signal Processing, IEEE Transaction on Wireless Communications等国际著名期刊审稿人。IEEE会员。


五、任课教师信息(包括主讲教师):

 任课

教师

 学科

(专业)

 办公

电话

 住宅

 电话

 手机

 电子邮件

 通讯地址

 邮政

 编码

康维

信息安全

83795112-868



Wkang79@gmail.com

江苏省南京市四牌楼2号李文正楼南413

210096




Application Form For Opening Graduate Courses

School (Department/Institute)School of Information Science and Engineering

Course Type: New Open     Reopen □   Rename □Please tick in □, the same below

Course Name

Chinese

信息安全数学基础

English

Mathematical Foundations of Information Security

Course Number


Type of Degree

Ph. D


Master

Total Credit Hours

54

In Class Credit Hours

54

Credit

3

Practice

0

Computer-using Hours

0

Course Type

Public FundamentalMajor Fundamental    □Major Compulsory     □Major Elective

School (Department)

School of Information Science and Engineering

Term

Autumn

Examination

A.PaperOpen-book   □ Closed-bookB. □Oral   

C. □Paper-oral Combination                       D. □ Others

Chief

Lecturer

Name

Wei Kang

Professional Title

Associate Researcher

E-mail

Wkang79@gmail.com

Website


Teaching Language used in Course

Chinese

Teaching Material Website


Applicable Range of Discipline

Second-class: Information Security

Name of First-Class Discipline

Information and Communication Engineering

Number of Experiment

0

Preliminary Courses


Teaching Books

Textbook Title

Author

Publisher

Year of Publication

Edition Number

Main Textbook

信息安全数学基础

陈恭亮

清华大学出版社

20046

1

Main Reference Books

信息安全数学基础

覃中平等

清华大学出版社

20068

1

信息安全数学基础

贾春福

南开大学出版社

20068

1

信息安全数学基础

李继国等

武汉大学出版社

20069

1

信息安全数学基础

谢敏

西安电子科技大学出版社

20068

1

代数

Michael Artin

机械工业出版社

20043

1

初等数论及其应用

Kenneth H. Rosen

机械工业出版社

20053

5


  1. Course Introduction (including teaching goals and requirements) within 300 words:

This course systematically introduces the knowledge in basic number theory and abstract algebra knowledge, which is necessary for the area of information security, including congruences, quadratic residues, primitive roots and exponents in number theory and groups, rings, fields and finite fields in algebra. This course will make the necessary foundation for the graduate students in their future studies and researches in the area of information security.




  1. Teaching Syllabus (including the content of chapters and sections. A sheet can be attached):

  1. Division

    1. Integer division

    2. The Euclidean algorithm

    3. Greatest Common Divisors

    4. The fundamental theorem of arithmetic

  2. Congruences

    1. Basic properties of congruences

    2. Complete system of residues and Complete set of residues

    3. Eulers theorem and Fermats little theorem

    4. Chinese remainder theorem

  3. Quadratic residues

    1. Legendre symbol

    2. Jacobi Symbol

    3. Quadratic residue equation

  4. Primitive roots and exponents

    1. Primitive roots

    2. Exponents

  5. Groups

    1. Groups

    2. Subgroups and cosets

    3. Quotient groups

    4. Homomorphisms and Isomorphisms

  6. Rings

    1. Rings

    2. Ideals and quotient rings

    3. Polynomial rings

  7. Fields

    1. Fields

    2. Finite fields

    3. Minimal polynomials and primitive polynomials

    4. Structure, representation and calculation of finite fields.


  1. Teaching Schedule:


Week

Course Content

Teaching Method

1

Integer division, The Euclidean algorithm

Class

2

Greatest Common Divisors, The fundamental theorem of arithmetic

Class

3

Basic properties of congruences, Complete system of residues and Complete set of residues

Class

4

Euler’s theorem and Fermat’s little theorem

Class

5

Chinese remainder theorem

Class

6

Legendre symbol

Class

7

Jacobi symbol

Class

8

Quadratic residue equation

Class

9

Primitive roots and exponents

Class

10

Groups

Class

11

Subgroups and cosets

Class

12

Quotient groups, Homomorphisms and Isomorphisms

Class

13

Rings, Ideals and quotient rings

Class

14

Polynomial rings

Class

15

Fields, Finite fields

Class

16

Minimal polynomials and primitive polynomials

Class

17

Structure, representation and calculation of finite fields

Class

18


Exam

Note: 1.Above one, two, and three items are used as teaching Syllabus in Chinese and announced on the Chinese website of Graduate School. The four and five items are preserved in Graduate School.


2. Course terms: Spring, Autumn , and Spring-Autumn term.  

3. The teaching languages for courses: Chinese, English or Chinese-English.

4. Applicable range of discipline: public, first-class discipline, second-class discipline, and third-class discipline.

5. Practice includes: experiment, investigation, research report, etc.

6. Teaching methods: lecture, seminar, practice, etc.

7. Examination for degree courses must be in paper.

8. Teaching material websites are those which have already been announced.

9. Brief introduction of chief lecturer should include: personal information (date of birth, gender, degree achieved, professional title), research direction, teaching and research achievements. (within 100-500 words)


  1. Brief Introduction of Chief lecturer:

Wei Kang, born at Aug. 1979, male, Ph.D., Associate Researcher. He finished his undergraduate study in Department of Electronic Engineering in Beijing University of Posts and Telecommunications with bachelor degree of engineering in 2001. He obtained his master degree of engineering in Department of Electrical and Computer Engineering in McGill University in Montreal, Canada in 2003, and Ph.D. degree in Department of Electrical and Computer Engineering in University of Maryland, College Park, U.S.A in 2008. From Jan. 2009, he is with the research center of information security in school of information science and engineering in Southeast University as a associate researcher. He is a member of technical program committee of Chinacom from 2008-2009. He isa reviewer for international journals, e.g., IEEE Transaction on Information Theory, IEEE Transaction on Communications, IEEE Transaction on Signal Processing, IEEE Transaction on Wireless Communications. He is a member of IEEE.


  1. Lecturer Information (include chief lecturer)


Lecturer

Discipline

(major)

Office

Phone Number

Home Phone Number

Mobile Phone Number

Email

Address

Postcode

Wei Kang

Information Security

83795112-868



Wkang79@gmail.com

2 Sipailou

Liwenzheng South 413

Nanjing, Jiangsu

210096







9