Tsuyoshi Takagi & Masato Wakayama 
Mathematical Modelling for Next-Generation Cryptography 
CREST Crypto-Math Project

This book presents the mathematical background underlying security modeling in the context of next-generation cryptography. By introducing new mathematical results in order to strengthen information security, while simultaneously presenting fresh insights and developing the respective areas of mathematics, it is the first-ever book to focus on areas that have not yet been fully exploited for cryptographic applications such as representation theory and mathematical physics, among others.


 


Recent advances in cryptanalysis, brought about in particular by quantum computation and physical attacks on cryptographic devices, such as side-channel analysis or power analysis, have revealed the growing security risks for state-of-the-art cryptographic schemes. To address these risks, high-performance, next-generation cryptosystems must be studied, which requires the further development of the mathematical background of modern cryptography. More specifically


, in order to avoid the security risks posed by adversaries with advanced attack capabilities, cryptosystems must be upgraded, which in turn relies on a wide range of mathematical theories.

 


This book is suitable for use in an advanced graduate course in mathematical cryptography, while also offering a valuable reference guide for experts.

Table of Content

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.

About the author

Tsuyoshi Takagi
Professor, Kyushu University, Institute of Mathematics for Industry 
Masato Wakayama
Professor, Kyushu University, Institute of Mathematics for Industry 
Keisuke Tanaka
Associate Professor, Tokyo Institute of Technology, Department of Mathematical and Computing Sciences 
Noboru Kunihiro
Associate Professor, The University of Tokyo, Graduate School of Frontier Sciences 
Kazufumi Kimoto
Professor, University of the Ryukyus, Department of Mathematical Sciences Dung Hoang Duong
Assistant Professor, Kyushu University, Institute of Mathematics for Industry