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This open access book presents selected papers from International Symposium on Mathematics, Quantum Theory, and Cryptography (MQC), which was held on September 25-27, 2019 in Fukuoka, Japan. The international symposium MQC addresses the mathematics and quantum theory underlying secure modeling of the post quantum cryptography including e.g. mathematical study of the light-matter interaction models as well as quantum computing. The security of the most widely used RSA cryptosystem is based on the difficulty of factoring large integers. However, in 1994 Shor proposed a quantum polynomial time algorithm for factoring integers, and the RSA cryptosystem is no longer secure in the quantum computing model. This vulnerability has prompted research into post-quantum cryptography using alternative mathematical problems that are secure in the era of quantum computers. In this regard, the National Institute of Standards and Technology (NIST) began to standardize post-quantum cryptography in 2016. This book is suitable for postgraduate students in mathematics and computer science, as well as for experts in industry working on post-quantum cryptography.

Applied mathematics. --- Engineering mathematics. --- Data structures (Computer science). --- Quantum computers. --- Computer security. --- Mathematical and Computational Engineering. --- Data Structures and Information Theory. --- Quantum Computing. --- Systems and Data Security. --- Computer privacy --- Computer system security --- Computer systems --- Computers --- Cyber security --- Cybersecurity --- Electronic digital computers --- Protection of computer systems --- Security of computer systems --- Data protection --- Security systems --- Hacking --- Information structures (Computer science) --- Structures, Data (Computer science) --- Structures, Information (Computer science) --- Electronic data processing --- File organization (Computer science) --- Abstract data types (Computer science) --- Engineering --- Engineering analysis --- Mathematical analysis --- Protection --- Security measures --- Mathematics --- Mathematical and Computational Engineering --- Data Structures and Information Theory --- Quantum Computing --- Systems and Data Security --- Mathematical and Computational Engineering Applications --- Data and Information Security --- Cryptography for Quantum Computers --- Post-quantum Cryptography --- Number Theory --- Representation Theory --- Quantum Physics --- Security Modelling --- Open Access --- Maths for engineers --- Algorithms & data structures --- Information theory --- Mathematical theory of computation --- Computer security --- Network security