Mathematical Modelling for Next-Generation Cryptography

1. Introduction to CREST Crypto-Math Project
Tsuyoshi Takagi

Part I. Mathematical Cryptography

2. Multivariate Public Key Cryptosystems
Yasufumi Hashimoto

3. Code-Based Zero-Knowledge Protocols and Their Applications
Kirill Morozov

4. Hash Functions Based on Ramanujan Graphs
Hyungrok Jo

5. Pairings on Hyperelliptic Curves with Considering Recent Progress on the NFS Algorithms
Masahiro Ishii

6. Efficient Algorithms for Isogeny Sequences and Their Cryptographic Applications
Katsuyuki Takashima

Part II. Mathematics Towards Cryptography

7. Spectral Degeneracies in the Asymmetric Quantum Rabi Model
Cid Reyes-Bustos, Masato Wakayama

8. Spectra of Group-Subgroup Pair Graphs
Kazufumi Kimoto

9. Ramanujan Cayley Graphs of the Generalized Quaternion Groups and the Hardy–Littlewood Conjecture
Yoshinori Yamasaki

10. Uniform Random Number Generation and Secret Key Agreement for General Sources by Using Sparse Matrices
Jun Muramatsu, Shigeki Miyake

11. Mathematical Approach for Recovering Secret Key from Its Noisy Version
Noboru Kunihiro

Part III. Lattices and Cryptography

12. Simple Analysis of Key Recovery Attack Against LWE
Masaya Yasuda

13. A Mixed Integer Quadratic Formulation for the Shortest Vector Problem
Keiji Kimura, Hayato Waki

14. On Analysis of Recovering Short Generator Problems via Upper and Lower Bounds of Dirichlet L-Functions: Part 1
Shingo Sugiyama

15. On Analysis of Recovering Short Generator Problems via Upper and Lower Bounds of Dirichlet L-functions: Part 2
Shinya Okumura

16. Recent Progress on Coppersmith’s Lattice-Based Method: A Survey
Yao Lu, Liqiang Peng, Noboru Kunihiro

Part IV. Cryptographic Protocols

17. How to Strengthen the Security of Signature Schemes in the Leakage Models: A Survey
Yuyu Wang, Keisuke Tanaka

18. Constructions for the IND-CCA1 Secure Fully Homomorphic Encryption
Satoshi Yasuda, Fuyuki Kitagawa, Keisuke Tanaka

19. A Survey on Identity-Based Encryption from Lattices
Goichiro Hanaoka, Shota Yamada

Keywords: Computer Science, Data Structures, Cryptology and Information Theory, Systems and Data Security, Appl.Mathematics/Computational Methods of Engineering, Number Theory, Quantum Field Theories, String Theory, Quantum Physics