Course Information
SemesterCourse Unit CodeCourse Unit TitleL+PCreditNumber of ECTS Credits
7MATH445MATHEMATICAL ASPECTS OF BLOCKCHAIN TECHNOLOGIES3+036

Course Details
Language of Instruction English
Level of Course Unit First Cycle
Department / Program MATHEMATICS
Mode of Delivery Face to Face
Type of Course Unit Elective
Objectives of the Course The course aims at introducing the mathematical aspects of the cryptography utilized in blockchain applications such as timestamps smart contracts, zksnarks, snark friendly hash functions such as MiMC, Poseidon, and threshold cryptography.
Course Content The general scope of the course consists of design principals and security analysis of cryptographic building blocks and protocols of block chain technologies and schemes.
Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator None
Name of Lecturers Associate Prof.Dr. Orhun Kara
Associate Prof.Dr. Berkant Ustao─člu
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources Cryptography: Theory and Practice, 3rd edition, CRC press, Douglas R. Stinson
Handbook of applied cryptography, CRC Press 1996, A.J.Menezes, P.C. Von Oorschot, S. A. Vanstone
Cryptographic Primitives in Blockchain Technology: A mathematical introduction, Oxford University Press (November 9, 2020), by Andreas Bolfing

Course Category

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Midterm exams 1 % 20
Quizzes 0 % 0
Homeworks 4 % 30
Other activities 0 % 0
Laboratory works 0 % 0
Projects 1 % 10
Final examination 1 % 40
Total
7
% 100

ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Weekly Course Time 42 1 42
Outside Activities About Course (Attendance, Presentation, Midterm exam,Final exam, Quiz etc.) 4 20 80
Application (Homework, Reading, Self Study etc.) 1 18 18
Exams and Exam Preparations 2 20 40
Total Work Load   Number of ECTS Credits 6 180

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 possesses a general concept of block chain technologies
2 possesses mathematical aspects of blockchain applications
3 understands the designs of privacy-preserving cryptocurrencies
4 understands the mathematics behind the cryptographic services in blockchains
5 understands the design criteria of smart contracts, CBDCs


Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 General overview of cryptography Cryptography: Theory and Practice, 3rd edition, CRC press, Douglas R. Stinson
2 Public key encryptions Cryptography: Theory and Practice, 3rd edition, CRC press, Douglas R. Stinson
3 Digital signatures and hash functions: ECDSA/EdDSA/BLS and PBKDF2/Scrypt/Bcrypt/ SHA256/Keccak/MiMC/Poseidon Cryptography: Theory and Practice, 3rd edition, CRC press, Douglas R. Stinson
4 Group signatures and ring signatures Cryptography: Theory and Practice, 3rd edition, CRC press, Douglas R. Stinson
5 Multiparty computations and Threshold Cryptography Cryptography: Theory and Practice, 3rd edition, CRC press, Douglas R. Stinson
6 Zero knowledge proofs: ZKSNARKs and STARKs Cryptographic Primitives in Blockchain Technology: A mathematical introduction, Oxford University Press (November 9, 2020), by Andreas Bolfing
7 Anonymous credentials (Self-Sovereign Identity) Cryptographic Primitives in Blockchain Technology: A mathematical introduction, Oxford University Press (November 9, 2020), by Andreas Bolfing
8 Commitment schemes Cryptographic Primitives in Blockchain Technology: A mathematical introduction, Oxford University Press (November 9, 2020), by Andreas Bolfing
9 Smart contracts and applications of distributed blockchains Cryptographic Primitives in Blockchain Technology: A mathematical introduction, Oxford University Press (November 9, 2020), by Andreas Bolfing
10 Cryptology of NFTs and tokens, distributed consensus problems Cryptographic Primitives in Blockchain Technology: A mathematical introduction, Oxford University Press (November 9, 2020), by Andreas Bolfing
11 Cryptographic structures of Bitcoin and Ethereum Cryptographic Primitives in Blockchain Technology: A mathematical introduction, Oxford University Press (November 9, 2020), by Andreas Bolfing
12 Cryptographic Architectures of Layer 2s (Optimistic Rollups, ZKRollups, ZKEVMs) Cryptographic Primitives in Blockchain Technology: A mathematical introduction, Oxford University Press (November 9, 2020), by Andreas Bolfing
13 Cryptographic structure of Zether Cryptographic Primitives in Blockchain Technology: A mathematical introduction, Oxford University Press (November 9, 2020), by Andreas Bolfing
14 Cryptographic structures of Monero and ZCash Cryptographic Primitives in Blockchain Technology: A mathematical introduction, Oxford University Press (November 9, 2020), by Andreas Bolfing


Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14
C1 1 2 2 4 2 4 3 3 3 2 2 2 1
C2 1 2 2 4 2 4 3 3 3 2 3 2 1
C3 2 3 2 4 3 4 3 3 3 2 3 4 2
C4 2 3 2 4 3 4 3 3 3 2 3 4 2
C5 2 3 2 4 3 4 2 3 3 2 2 2 1

Contribution: 0: Null 1:Slight 2:Moderate 3:Significant 4:Very Significant


https://obs.iyte.edu.tr/oibs/bologna/progCourseDetails.aspx?curCourse=227347&lang=en