This open access book presents mathematical foundations for cryptography securely used in the era of quantum computers. In particular, this book aims to deepen the basic mathematics of post-quantum cryptography, model the strongest possible attacks such as side-channel attacks, and construct cryptographic protocols that guarantee security against such attacks. This book is a sequel of the successful book entitled by ``Mathematical Modeling for Next-Generation Cryptography - CREST Crypto-Math Project'' which was published in 2018. The book is suitable for use in an advanced graduate course in mathematical cryptography and as a reference book for experts.