數論與密碼學
課程編號: SAYT1114
上課日期: 15/8, 16/8, 18/8, 19/8, 22/8, 23/8, 25/8, 26/8, 29/8, 2022
上課時間: 10:30am – 5:15pm
考試日期: 31/8/2022 (10:30am-1:30pm)
後備課堂日期: 20/8, 27/8, 3/9, 2022 (10:30am – 5:15pm)
上課地點: [中文大學, 詳情有待公佈]*
任教導師: 廖振隆博士 (香港中文大學)
大學認可: 中文大學2學分
教學語言：粵語為主，附以英文教材
對象: 準備升上中四或中五的同學，學員須具備良好的抽象數學推理能力。
內容簡介:在課程的前半部份，我們會先介紹一下數論的一些基本知識，包括取模運算，歐拉定理。之後我們將討論研究密碼學不可或缺的兩個數論中的題材：質數測試和原根。在課程的後半部份，我們將探討數論在密碼學中的應用，包括一些經典系統，例如維吉尼亞密碼，以及一些較現代的系統，例如數據加密標準，RSA演算法，數位簽章。我們還會概括地討論一下秀爾演算法：一個基於量子力學的算法和量子密鑰分發：一個基於量子力學的密碼系統。
學費: 港幣 3,990元正 (已包含港幣40元申請費用)**
備註
*此課程暫定於中文大學內授課，或有可能轉為線上授課，視乎實際情況而定。
**如課程最終轉為線上授課，學費將會調整為港幣 3,040元正 (已包含港幣40元申請費用) 。
Number Theory and Cryptography
Course code: SAYT1084
15/8, 16/8, 18/8, 19/8, 22/8, 23/8, 25/8, 26/8, 29/8, 2022
Time: 10:30am – 5:15pm
Examination Date: 31/8/2022 (10:30am-1:30pm)
Reserved Date: 20/8, 27/8, 3/9, 2022 (10:30am – 5:15pm)
Venue: [CUHK. Detail to be announced]*
Lecturer: Dr. Liu Chun Lung Kelvin (CUHK)
University Recognition: 2 credits of CUHK
Medium of Instruction: mainly in Cantonese with English course materials
Expected applicants: : Students advancing to Secondary 4 or 5, and have high competence in abstract mathematical reasoning.
Introduction: In the first half, we will cover some basic knowledge in Number Theory, including modular arithmetic and Euler’s theorem. Then, we will cover two topics in Number Theory: primality test and primitive root, which are indispensable in studying Cryptography. In the second half, we will explore some applications of Number Theory in Cryptography, including some classical systems such as Vigenere cipher and some modern systems such as DES, RSA, digital signature. We will also briefly discuss Shor’s algorithm: a quantum-based algorithm and QKD: a quantum-based cryptosystem.
Tuition fee: HK$3,990 (with $40 application fee included)**
Remark:
*This course offers face-to-face lessons on CUHK campus. It may switch to online teaching, subject to the actual situation.
**The tuition fee will be adjusted to HK$3,040 (with $40 application fee included) if the course finally switches to online teaching.
網上報名(Online application)
入學試免試條款 Conditions for Admission Screening Test Exemption
凡符合以下其中一項條款的申請人，可免除入學試而獲本科直接取錄。（參考附註）
Applicants who satisfy either one of the following condition may be exempted from Admission Screening Test and will be directly admitted into this course. (refer to note below)
- 曾修讀並及格完成以下任何一個科目取錄: 「複數的幾何面貌」、「複數與解析幾何」、「近世代數初探」。
Passed in any of the following courses before: Geometric Perspectives of Complex Numbers, Complex Number and Analytical Geometry, and Towards Modern Algebra.
- 曾獲得以下任何一個科目取錄:「數論與密碼學」、「微分幾何初探」、「數學分析入門」、「非歐幾何賞析」。
Being admitted in one of the following courses before: Number Theory and Cryptography, Towards Differential Geometry, Mathematical Analysis, and Understanding Non-Euclidean Geometry.
（參考附註 note）
曾修讀「數學啟導修習I或II」的學生，仍須參加入學試，但可獲優先考慮。
Those who had taken "Enrichment Mentoring Mathematics I or II" still need to sit the Test, but will be considered with priority.
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