## 1 Introduction  
### Central Bank Digital Currency  
Physical cash, paper notes, and coins have been the key medium of exchange in conventional financial systems for a long time [1]. However, in the last few decades, due to the growth of the internet and communication technologies, physical cash has been losing its preeminence [1]. Electronic financial systems have become widespread, with digital numbers on computers representing money rather than physical cash. It is a well-known fact that monetary policies, such as the open market operation, quantitative easing (QE), or quantitative tightening (QT), are executed not by printing or collecting paper notes but by using electronic funds created with keystrokes on computers [2, 3]. The changes can be seen more easily in the retail sector. Technological advances are deregulating the financial industry, and many people have already become used to various payment methods operated by various entities, such as credit cards, online banking services, mobile payments, etc. [1, 4, 5]. Some countries are already at the stage of a so-called \"cashless society\" [6]. In 2016, the share of cash used for all payments in South Korea was only 14%; in China, 18%; and in the UK, 24%. The share of cash used in the United States in 2020 was 19% [7, 8, 9]. Electronic financial systems are considered to have advantages compared to conventional financial systems mainly for two reasons. First, electronic financial systems are considered to be more transparent than conventional financial systems. Unlike conventional financial systems based on physical cash, which has the characteristic of anonymity, in electronic financial systems, transactions between users can be watched and logged. Therefore, malicious users and unlawful acts can be traced and detected. Second, electronic financial systems can enable flexible and easy use of money and help vitalize the economy. In countries where electronic financial systems are in use, people can use bank services and join in e-commerce anytime and anywhere they want, as the digital currency used in the systems is free from physical constraints. This could increase the amount of currency in circulation and contribute to economic stabilization [10]. Even with these advantages, electronic financial systems still have some defects to be compensated for. First, electronic financial systems usually have charges for using the system, resulting in an additional cost to use money or currency [11]. For example, credit card networks routinely charge card fees of 3% [11]. E-wallet (electronic wallet) services managed by Sticpay charge 1-3.85% of deposit fees [12]. Such high charges can attenuate economic activity and commerce [11]. Second, without proper security policies, personal data breaches can occur in electronic financial systems. Electronic financial systems are vulnerable to digital attacks by their nature. Access to the systems via the internet, or any other possible measures, is open to anonymous users at all times. Further, when personal data breaches occur, the quantity of data breached at once could be large. In 2019, when Capital One, the fifth largest credit card issuer in the United States, was hacked, the personal data of 106 million customers were leaked [13]. In 2014, the user information of at least 20 million people was leaked in Korea, a country of 50 million [14]. Third, in electronic financial systems, the problem of financial exclusion, which refers to individuals and populations without access to common financial services, can occur. For instance, China is a country where electronic financial systems such as Alipay and Wechat are widely used. However, China's rural and farm communities use internet technologies only half as much as all users, and less than 2% access credit through the internet [15]. Additionally, many commercial electronic financial systems are closed to people with low credit ratings [16]. As a solution to these problems, many countries are considering central bank digital currency (CBDC).