Angou to Ryoshi-Computer (Cryptography and Quantum Computing - Introduction to Quantum-Resistant Cryptography)

Cryptography is prevalent in various aspects of our life and is gaining importance as a core technology supporting security in the information society. For example, without cryptography, safe online shopping and virtual currency using blockchain would not be possible. It is important to conduct strict security evaluations to use cryptography as an infrastructure for information technology. The security of currently popular encryption methods has been carefully evaluated from various perspectives by researchers in the field of cryptography, and therefore, those methods can be used confidently. However, quantum computers, whose computing power is said to surpass that of conventional computers, may threaten the security of cryptographic technologies already in widespread use. Therefore, research and development of cryptographic techniques that can be used securely even in the era of quantum computers is being actively promoted worldwide.
 
This book examines in detail the impact of quantum computers on cryptography from various perspectives. You may have heard of RSA encryption, which is widely used for online shopping. The security of RSA encryption relies on the difficulty of mathematical problems, including factoring large numbers—it uses 617 digits, which is a huge number, and it is estimated that cracking such a cipher would take at least 30 years of computation even with a supercomputer. However, this factoring can be done much more quickly with a quantum computer. This is called a cryptographic compromise. In other words, quantum computers may compromise RSA encryption. For this reason, research and development and standardization of quantum-resistant cryptography, which would be secure even from a quantum computer, are progressing.
 
This book provides a detailed explanation of quantum-resistant cryptography, a research topic discussed in academia for more than 40 years, since the late 1970s. In August 2015, the National Security Agency suddenly issued a statement on the transition to quantum-resistant cryptography, and in 2016, the National Institute of Standards and Technology started standardization activities for it; these developments have put the spotlight on quantum-resistant cryptography—it relies on mathematical problems for which there is no known quantum computer-powered fast calculation method. This book explains five representative mathematical problems and the cryptographic methods (lattice-based cryptography, code-based cryptography, multivariate polynomial cryptography, hash function signatures, and isogeny-based cryptography) constructed based on those problems. In particular, the book provides an in-depth explanation of the specific methods of constructing encryption schemes using the mathematical problems underlying multivariate polynomial cryptography and lattice-based cryptography.
 

(Written by TAKAGI Tsuyoshi, Professor, Graduate School of Information Science and Technology / 2022)