Mathematical Foundations for Post-Quantum Cryptography -

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Résumé :
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....

Biographie:

Tsuyoshi Takagi is a professor in the Department of Mathematical Informatics at the University of Tokyo. His current research interests are information security and cryptography. He received the Ph.D. from the Technical University of Darmstadt in 2001. He received IEICE Achievement Award in 2013 and JSPS Prize in 2014. He was a program chair of the 7th International Conference on Post-Quantum Cryptography, PQCrypto 2016.

Masato Wakayama is the Fundamental Mathematics Research principal of NTT Institute for Fundamental Mathematics in Nippon Telegraph and Telephone Corporation. He also serves as a principal fellow at Center for Research and Development Strategy of Japan Science and Technology Agency and a professor emeritus at Institute of Mathematics for Industry of Kyushu University. His current research interests are representation theory and its applications to number theory and quantum physics. He received the Ph.D. from Hiroshima University in 1985. He received Nice-Step-Researcher Award in 2007 by Ministry of Education, Culture, Sports, Science, and Technology (MEXT). He also managed various research projects on mathematics for industry such as Global COE Program Education and Research Hub for Mathematics-for-Industry by MEXT.

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Sommaire:

1. Algebraic Geometry.- 2. Number Theory.- 3. Theory of Computation.- 4. Quantum Computation.- 5. Quantum Field Theory.- 6. Mathematical Physics.- 7. Representation Theory.- 8. Lattice Theory.- 9. Multivariate Polynomial Theory.- 10. Data Encryption.- 11. Digital Signature.- 12. Searchable Encryption.- 13. Obfuscation.- 14. Privacy Protection.- 15. Copyright Protection.- 16. ID-based Encryption.