Mathematical modelling for next-generation cryptography : Crest Crypto-math Project

Description

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. Read more... Abstract: 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 Front Matter ....Pages i-viii Introduction to CREST Crypto-Math Project (Tsuyoshi Takagi)....Pages 1-14 Front Matter ....Pages 15-15 Multivariate Public Key Cryptosystems (Yasufumi Hashimoto)....Pages 17-42 Code-Based Zero-Knowledge Protocols and Their Applications (Kirill Morozov)....Pages 43-62 Hash Functions Based on Ramanujan Graphs (Hyungrok Jo)....Pages 63-79 Pairings on Hyperelliptic Curves with Considering Recent Progress on the NFS Algorithms (Masahiro Ishii)....Pages 81-96 Efficient Algorithms for Isogeny Sequences and Their Cryptographic Applications (Katsuyuki Takashima)....Pages 97-114 Front Matter ....Pages 115-115 Spectral Degeneracies in the Asymmetric Quantum Rabi Model (Cid Reyes-Bustos, Masato Wakayama)....Pages 117-137 Spectra of Group-Subgroup Pair Graphs (Kazufumi Kimoto)....Pages 139-157 Ramanujan Cayley Graphs of the Generalized Quaternion Groups and the Hardy–Littlewood Conjecture (Yoshinori Yamasaki)....Pages 159-175 Uniform Random Number Generation and Secret Key Agreement for General Sources by Using Sparse Matrices (Jun Muramatsu, Shigeki Miyake)....Pages 177-198 Mathematical Approach for Recovering Secret Key from Its Noisy Version (Noboru Kunihiro)....Pages 199-217 Front Matter ....Pages 219-219 Simple Analysis of Key Recovery Attack Against LWE (Masaya Yasuda)....Pages 221-238 A Mixed Integer Quadratic Formulation for the Shortest Vector Problem (Keiji Kimura, Hayato Waki)....Pages 239-255 On Analysis of Recovering Short Generator Problems via Upper and Lower Bounds of Dirichlet L-Functions: Part 1 (Shingo Sugiyama)....Pages 257-278 On Analysis of Recovering Short Generator Problems via Upper and Lower Bounds of Dirichlet L-functions: Part 2 (Shinya Okumura)....Pages 279-295 Recent Progress on Coppersmith’s Lattice-Based Method: A Survey (Yao Lu, Liqiang Peng, Noboru Kunihiro)....Pages 297-312 Front Matter ....Pages 313-313 How to Strengthen the Security of Signature Schemes in the Leakage Models: A Survey (Yuyu Wang, Keisuke Tanaka)....Pages 315-330 Constructions for the IND-CCA1 Secure Fully Homomorphic Encryption (Satoshi Yasuda, Fuyuki Kitagawa, Keisuke Tanaka)....Pages 331-347 A Survey on Identity-Based Encryption from Lattices (Goichiro Hanaoka, Shota Yamada)....Pages 349-365 Back Matter ....Pages 367-368