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Subject | Information & Data Science, Natural Science
Cryptology Today―An Introduction to Modern Cryptography
- Modern Cryptography
- Data Science
- Blockchain Technology
- Digital Signature
- Quantum Computer
Cryptography is a technology with a history spanning thousands of years, but it has undergone fundamental and rapid transformation since the 1970s. Today, the science and technology of cryptography have become deeply embedded in our daily lives in various forms. This is referred to as Modern Cryptography. In this course, we will introduce the key points—in simple terms—regarding the principles and characteristics of modern cryptography, its basic functions, its relationship with social infrastructure, and the functions that will be required of cryptography in the near future. Through this, we will also gain a glimpse into the present and future of the information society, using cryptography as a lens. Although modern cryptography is based on mathematical theory, we will strive to provide explanations that are as intuitive as possible.
©Tohoku University. Last Update
2026-09-14
Content／学習内容
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In Week 1, we will explain the mathematical mechanisms underlying the security of modern cryptography. These are one-way functions, which have the property of being easy to compute in the forward direction but hard to compute the inverse. By learning examples of representative cryptographic schemes based on this property, we will deepen our understanding of the basic principles of modern cryptography.
- 1-1. Introduction
- 1-2. One-way function 1: Prime factorization problem
- 1-3. One-way function 2: RSA problem
- 1-4. One-way function 3: Discrete logarithm problem
- 1-5. Hash function and Pseudorandom Number Generator
- 1-6. Diffie-Hellman key exchange
- 1-7. ElGamal Cryptosystem
- 1-8. RSA Cryptosystem
- 1-9. RSA signature scheme
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In Week 2, we will learn that by utilizing the tools introduced in Week 1, we can achieve various functions that serve as components for constructing large-scale and secure information systems. Specifically, these include digital signatures, identity authentication, secret computation that performs arithmetic operations while data remains encrypted, mechanisms to distribute and share secret information among multiple people, and zero-knowledge proofs that prove possession of a password without revealing it.
- 2-1. Introduction
- 2-2. Digital Signature 1 - Basic Signature Method
- 2-3. Digital Signature 2 - Group Signature and Blind Signature
- 2-4. Secret Sharing - Mechanism and Typical Methods
- 2-5. Secret Computation - Homomorphic Encryption and Its Applications
- 2-6. Zero-Knowledge Proof 1 - Intuitive Explanation of Basic Functions
- 2-7. Zero-Knowledge Proof 2 - Somewhat Formal Explanation
- 2-8. Zero-Knowledge Proof 3 - Specific Example of Proof
- 2-9. Zero-Knowledge Proof 4 - Limits of Proof
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In Week 3, we will learn how a massive global social infrastructure is woven together through the advanced combination and ingenious operation of several types of cryptography. Specifically, we will focus on PKI, which ensures the trustworthiness of websites; SSL/TLS, which protects communications; and crypto assets, which are increasing their presence in the global economy.
- 3-1. Introduction
- 3-2. Internet −IPSec, TLS
- 3-3. Public Key Infrastructure −PKI
- 3-4. Electronic Money−Transportation IC Card etc.
- 3-5. Blockchain１ −The Big Picture and Crypto Asset
- 3-6. Blockchain２ −Working Principle and Operating Mechanism
- 3-7. Blockchain３ −Use Case：NFT
- 3-8. Blockchain４ −Use Case：Smart Contract
- 3-9. Blockchain５ −Hopes and Issues as Social Infrastructure
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In Week 4, we will learn about the essential challenges faced by modern cryptography and the current state of efforts to solve them. In fact, it is known that in the near future, when quantum computers become a practical reality, functions currently considered to be one-way will no longer be so. Therefore, attempts to construct one-way functions for a new era using computational problems that are considered hard even for quantum computers are gaining momentum. We will conclude the course by introducing representative examples of these and discussing the future.
- 4-1. Introduction
- 4-2. Classical and Quantum Computers – Basic Differences
- 4-3. Shore’s Algorithm – Solution to the Prime Factorization Problem
- 4-4. Candidates for Post-Quantum Cryptography – Classification by Relying Problems
- 4-5. Lattice Problems 1 – The Shortest Vector Problem
- 4-6. Lattice Problems 2 – The Learning with Errors Problem
- 4-7. Lattice Cryptography 1– Standardization Trends by the U.S. National Institute of Standards and Technology
- 4-8. Lattice Cryptography 2 – Overview of Standard Candidate Schemes
- 4-9. Future Outlook – Conclusion
Staff／スタッフ
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Hiroki ShizuyaTohoku University Institute for Excellence in Higher EducationPresident-Appointed Extraordinary Professor -
- Teacher
Masao SakaiTohoku University Center for Data-driven Science and Artificial IntelligenceAssociate Professor -
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Shuji IsobeTohoku University Center for Data-driven Science and Artificial IntelligenceAssociate Professor -
- Teacher
Eisuke KoizumiTohoku University Center for Data-driven Science and Artificial IntelligenceAssistant Professor -
- Teacher
Shingo HasegawaFukushima University Faculty of Symbiotic Systems ScienceProfessor
Contact／お問合せ先
Center for the Advancement of Open Online Education, Tohoku University
Email: secretary.mooc@grp.tohoku.ac.jp
