Cryptography, with a history dating back thousands of years, has undergone a radical and radical transformation since the 1970s, and today the science and technology of cryptography has become deeply embedded in our daily lives in many forms. This is called modern cryptography. This course introduces the principles and characteristics of modern cryptography, its basic functions, its relationship to social infrastructures, and the functions of cryptography that will be required in the near future. It will also provide a glimpse into the present and future of the information society using cryptography as a starting point. Although modern cryptography is based on mathematical theory, we will try to explain it as intuitively as possible and use the language of high school “Mathematics I” and “Mathematics A” when defining notations and concepts.

The first week will explain the mathematical mechanism underlying the security of modern cryptography. It is the one-way function, which has the property that computation in the forward direction is easy, but computation in the reverse direction is difficult. We will study examples of typical cryptographic schemes based on this property and deepen our understanding of the basic principles of modern cryptography.

In the second week, students will learn how various functions can be achieved using the tools from the previous week, which are the components of a large-scale, secure information system. Specifically, these include signatures and identity authentication in place of seals, secret calculations that perform four arithmetic operations while data is encrypted, mechanisms for distributing and sharing secret information among multiple people, and zero-knowledge proof of possession itself without showing a PIN.

In Week 3, you will learn about the current situation in which a huge global social infrastructure is woven by the sophisticated combination and clever operation of several cryptographic techniques. Specifically, we will focus on PKI to ensure the trustworthiness of websites, SSL/TLS to protect communications, and cryptographic assets that are increasingly present in the global economy.

In Week 4, you will learn about the essential challenges facing modern cryptography and the current status of efforts to solve them. In fact, it is known that in the near future, when quantum computers are put to full-scale practical use, functions that are currently considered unidirectional will no longer be so. Therefore, attempts to construct unidirectional functions for the new era using computational problems that are considered difficult even for quantum computers are gaining momentum. We will introduce some representative examples of these efforts and close the lecture by connecting them to the future.

*This course has the same content as the first course offered in January 2024 and the second course offered in January 2025, with some changes in assignments.