Post-Quantum Cryptography

Front Cover
Daniel J. Bernstein, Johannes Buchmann, Erik Dahmen
Springer Science & Business Media, Feb 1, 2009 - Mathematics - 246 pages

Quantum computers will break today's most popular public-key cryptographic systems, including RSA, DSA, and ECDSA. This book introduces the reader to the next generation of cryptographic algorithms, the systems that resist quantum-computer attacks: in particular, post-quantum public-key encryption systems and post-quantum public-key signature systems.

Leading experts have joined forces for the first time to explain the state of the art in quantum computing, hash-based cryptography, code-based cryptography, lattice-based cryptography, and multivariate cryptography. Mathematical foundations and implementation issues are included.

This book is an essential resource for students and researchers who want to contribute to the field of post-quantum cryptography.

 

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Contents

Introduction to postquantum cryptography
1
2 A taste of postquantum cryptography
6
3 Challenges in postquantum cryptography
11
4 Comparison to quantum cryptography
13
Quantum computing
15
3 The quantum Fourier transform
22
4 The hidden subgroup problem
25
5 Search algorithms
29
4 Codes and structures
116
5 Practical aspects
127
6 Annex
137
References
141
Latticebased Cryptography
147
2 Preliminaries
152
3 Finding Short Vectors in Random qary Lattices
154
4 Hash Functions
157

6 Outlook
31
References
32
Hashbased Digital Signature Schemes
35
1 Hash based onetime signature schemes
36
2 Merkles tree authentication scheme
40
3 Onetime keypair generation using an PRNG
44
4 Authentication path computation
46
5 Tree chaining
69
6 Distributed signature generation
73
7 Security of the Merkle Signature Scheme
81
References
91
Codebased cryptography
94
2 Cryptosystems
96
3 The security of computing syndromes as oneway function
106
5 Public Key Encryption Schemes
165
6 Digital Signature Schemes
180
7 Other Cryptographic Primitives
185
8 Open Questions
186
References
187
Multivariate Public Key Cryptography
192
2 The Basics of Multivariate PKCs
194
3 Examples of Multivariate PKCs
198
4 Basic Constructions and Variations
202
5 Standard Attacks
215
6 The Future
229
References
234
Index
242
Copyright

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About the author (2009)

Daniel J. Bernstein is a research professor in the Department of Computer Science at the University of Illinois at Chicago. Professor Bernstein has received a U.S. National
Science Foundation CAREER award, a Cyber Trust award, three more U.S.government grants, and a Sloan Research Fellowship for his research in computational number theory, cryptography, and computer security. He is the author of several dozen papers and two of the Internet's most popular server software packages, djbdns and qmail.

Johannes A. Buchmann is a Professor of Computer Science and Mathematics at the Technische Universitšt Darmstadt and an associate editor of the Journal of Cryptology. He received the most prestigious award in science in Germany, the Leibniz Award of the German Science Foundation. He also received the Karl Heinz-Beckurts Award for technology transfer. He is a member of the German Academy of Science and Engieneering.

Erik Dahmen is a PhD student in Prof. Buchmann's research group at the Technische Universitšt Darmstadt. He received his diploma degree in Mathematics from the Technische Universitšt Darmstadt in 2006. Erik Dahmen is the author of various research papers on hash-based cryptography.