Mathematical Modelling for Next-Generation Cryptography

CREST Crypto-Math Project

  • Tsuyoshi Takagi
  • Masato Wakayama
  • Keisuke Tanaka
  • Noboru Kunihiro
  • Kazufumi Kimoto
  • Dung Hoang Duong

Part of the Mathematics for Industry book series (MFI, volume 29)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Tsuyoshi Takagi
    Pages 1-14
  3. Mathematical Cryptography

  4. Mathematics Towards Cryptography

  5. Lattices and Cryptography

  6. Cryptographic Protocols

    1. Front Matter
      Pages 313-313
    2. Satoshi Yasuda, Fuyuki Kitagawa, Keisuke Tanaka
      Pages 331-347
    3. Goichiro Hanaoka, Shota Yamada
      Pages 349-365
  7. Back Matter
    Pages 367-368

About this book


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.


Next-generation Cryptographic Systems Shortest Vector Problem Quantum Interaction Models Noise Models Cryptographic Primitives Multivariate Quadratic Equations

Editors and affiliations

  • Tsuyoshi Takagi
    • 1
  • Masato Wakayama
    • 2
  • Keisuke Tanaka
    • 3
  • Noboru Kunihiro
    • 4
  • Kazufumi Kimoto
    • 5
  • Dung Hoang Duong
    • 6
  1. 1.Kyushu UniversityFukuokaJapan
  2. 2.Kyushu UniversityFukuokaJapan
  3. 3.Tokyo Institute of TechnologyTokyoJapan
  4. 4.The University of TokyoKashiwaJapan
  5. 5.University of the RyukyusNakagami-gunJapan
  6. 6.Institute of Mathematics for IndustryKyushu UniversityFukuokaJapan

Bibliographic information

  • DOI
  • Copyright Information Springer Nature Singapore Pte Ltd. 2018
  • Publisher Name Springer, Singapore
  • eBook Packages Engineering Engineering (R0)
  • Print ISBN 978-981-10-5064-0
  • Online ISBN 978-981-10-5065-7
  • Series Print ISSN 2198-350X
  • Series Online ISSN 2198-3518
  • Buy this book on publisher's site
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