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2016　Theory of Cryptography

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Academic unit or major
Graduate major in Mathematical and Computing Science
Instructor(s)
Tanaka Keisuke  Watanabe Osamu 
Class Format
Lecture     
Media-enhanced courses
Day/Period(Room No.)
Mon3-4(W832)  Thr3-4(W832)  
Group
-
Course number
MCS.T508
Credits
2
Academic year
2016
Offered quarter
3Q
Syllabus updated
2016/4/27
Lecture notes updated
-
Language used
English
Access Index

Course description and aims

This course gives an introduction of the theory of cryptography. The topics discussed in this course include coin-flipping protocol, computational complexity, secret-key encryption, public-key encryption, stream cipher, block cipher, mode of operation, message authentication code, RSA encryption, extended Euclidean algorithm, primality test, Chinese remainder theorem, RSA-OAEP, random oracle, hash function, signature, RSA-FDH, identification, zero-knowledge proof.
This course aims to help students to understand models, schemes, proofs appeared in the above topics. By understanding the contents of this course, students will also understand the basics of information security and cybersecurity for computer software, hardware, and network.

Student learning outcomes

By the end of this course, students will be able to understand:
1) models in cryptography
2) systems and algorithms in cryptography
3) techniques for security proofs in cryptography.

Keywords

cryptography, security, information security, cybersecurity, coin-flipping protocol, computational complexity, secret-key encryption, public-key encryption, stream cipher, block cipher, mode of operation, message authentication code, RSA encryption, extended Euclidean algorithm, primality test, Chinese remainder theorem, RSA-OAEP, random oracle, hash function, signature, RSA-FDH, identification, zero-knowledge proof

Competencies that will be developed

✔ Specialist skills Intercultural skills Communication skills ✔ Critical thinking skills ✔ Practical and/or problem-solving skills

Class flow

The class offers either a standard lecture or that with exercise. A lecture with exercise includes supplementary materials and the answers for the quizzes. Each class gives quizzes on the contents of the previous classes.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Overview of this course, the coin-flipping protocol, relation between cryptography and complexity theory Understand the description of the coin-flipping protocol
Class 2 Models and security properties of secret-key encryption and public-key encryption Understand the models and the security properties.
Class 3 Modes of operations on secret-key encryption and message authentication code Understand the properties of the modes of operations and the notion of message authentication code 概念について理解する。 Understanding its notion.
Class 4 Exercise-style lecture on simple cryptographic protocols Understand the schemes of simple cryptographic protocols
Class 5 Mathematical backgrounds for the RSA encryption scheme Understand the elements appeared in the RSA encryption scheme
Class 6 The extended Euclidean algorithm and the key generation algorithm of the RSA encryption scheme Understand the scheme and the analysis of the extended Euclidean algorithm
Class 7 Primality tests, the Chinese remainder theorem, the decryption of the RSA encryption scheme Understand the relation between the RSA encryption scheme and the Chinese remainder theorem
Class 8 Security of the RSA encryption scheme, the random oracle model Understand the notion of the random oracle model
Class 9 Exercise-style lecture on the RSA encryption scheme Understand the properties of the RSA encryption scheme
Class 10 The Elgamal encryption scheme and its security proof by reduction Understand the notion of reduction
Class 11 Signature Understand the notion and the schemes of signature
Class 12 Identification Understand the notion and the schemes of identification
Class 13 Zero-knowledge proofs Understand the notion and the schemes of zero-knowledge proofs
Class 14 Exercise-style lecture on signature and identification Understand the schemes and the security properties of signature and identification
Class 15 Advanced topics Understand the advanced topics

Textbook(s)

References will be announced in the first class.

Reference books, course materials, etc.

References will be announced in the first class.

Assessment criteria and methods

The evaluation consists of the quizzes in classes (60%) and the final exam (40%).

Related courses

  • MCS.T213 ： Introduction to Algorithms and Data Structures
  • MCS.T214 ： Theory of Automata and Languages
  • MCS.T323 ： Theory of Computation
  • MCS.T411 ： Computational Complexity Theory
  • MCS.T405 ： Theory of Algorithms

Prerequisites (i.e., required knowledge, skills, courses, etc.)

It is preferable to have the knowledge on the basics of algorithms and data structures, the theory of automata and languages, and the theory of computation.

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