課程名稱 |
橢圓曲線密碼學 Elliptic Curve Cryptography |
開課學期 |
104-1 |
授課對象 |
理學院 數學系 |
授課教師 |
陳君明 |
課號 |
MATH5012 |
課程識別碼 |
221 U6690 |
班次 |
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學分 |
3 |
全/半年 |
半年 |
必/選修 |
選修 |
上課時間 |
星期二8,9,10(15:30~18:20) |
上課地點 |
天數102 |
備註 |
總人數上限:80人 |
Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1041MATH5012_ECC |
課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
The study of elliptic curves by algebraists, algebraic geometers and number theorists dates back to the middle of the nineteenth century. Much attention has recently been focused on the use of elliptic curves in public key cryptography, first proposed in the work of Neal Koblitz and Victor Miller in 1985. Elliptic curve cryptography (ECC) is an exciting technology because for the same level of security as public-key cryptosystems such as RSA, it offers the benefits of smaller key sizes and hence of smaller memory and processor requirements. This makes them ideal for use in smart cards and other environments where resources such as storage, time, or power are at a premium. In the coming era of Internet of Things (IoT), the popularity of ECC is predicted to be significantly increased.
The Weil and Tate pairings on elliptic curves are used to construct protocols which cannot be implemented in another way. The most spectacular example of this is the identity-based encryption algorithm of Boneh and Franklin. Not only these protocols but also how these pairings can be efficiently implemented will be introduced.
The following topics will be brought to this course:
* Elliptic curve arithmetic
* Elliptic curves over finite fields
* Elliptic curve discrete logarithm problem
* Elliptic curve cryptography
* Elliptic curve factorization algorithm
* Efficient implementation of elliptic curves
* Determining the group order
* Bilinear pairings on elliptic curves
* Pairing-based cryptography
* Provable security of ECDSA
* Side-channel attacks and countermeasures
* Hyperelliptic curve cryptography |
課程目標 |
The course is designed for a wide audience ranging from a student majoring mathematics who knows about elliptic curves (or has been acquainted with them) wants a quick survey of the main results pertaining to cryptography, to an implementer who requires some knowledge of elliptic curve mathematics for use in a practical cryptosystem. Most of the important points such as implementation issues, security issues and point counting issues can be acquired with only a moderate understanding of the underlying mathematics. A flavor of the mathematics involved will be given for those who are interested. |
課程要求 |
已修過「代數導論」或「密碼學導論」 |
預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
"An Introduction to Mathematical Cryptography" by Jeffrey Hoffstein, Jill Pipher, and Joseph H. Silverman. Springer-Verlag – Undergraduate Texts in Mathematics. ISBN: 978-1-4939-1710-5 – 2nd edition – 2014
http://link.springer.com/book/10.1007/978-1-4939-1711-2 |
參考書目 |
* "Elliptic Curves in Cryptography" by Ian F. Blake, Gadiel Seroussi, and Nigel
P. Smart. London Mathematical Society Lecture Note Series. Cambridge University
Press, 1999. ISBN: 0521653746
* "Advances in Elliptic Curve Cryptography" edited by I.F. Blake, G. Seroussi
and N.P. Smart. London Mathematical Society Lecture Note Series. Cambridge
University Press, 2004. ISBN: 052160415X
* "Elliptic Curves: Number Theory and Cryptography" by Lawrence C. Washington.
2nd edition. CRC Press, 2008. Chapman and Hall/CRC. ISBN: 9781420071467
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評量方式 (僅供參考) |
No. |
項目 |
百分比 |
說明 |
1. |
Homework |
50% |
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2. |
Quiz |
10% |
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3. |
Midterm Exam |
20% |
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4. |
Final Exam or Report |
20% |
|
|
週次 |
日期 |
單元主題 |
第1週 |
9/15 |
Introduction with Bitcoin |
第2週 |
9/22 |
ECC Tutorial |
第3週 |
9/29 |
(颱風假) |
第4週 |
10/06 |
Quiz |
第5週 |
10/13 |
SAGE for ECC |
第6週 |
10/20 |
HW 1 due |
第7週 |
10/27 |
Imperfect Forward Secrecy |
第8週 |
11/03 |
Discrete Logarithm Problem |
第11週 |
11/24 |
Pairing-Based Cryptography |
第12週 |
12/01 |
Introduction to Pairings |
第13週 |
12/08 |
Introduction to MOV Attack |
第15週 |
12/22 |
Pairings in Practice |
第16週 |
12/29 |
Side-Channel Attacks and Countermeasures for ECC |
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