Post-Quantum Cryptography (eBook)

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. NationalScience 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 Universität 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 Universität Darmstadt. He received his diploma degree in Mathematics from the Technische Universität Darmstadt in 2006. Erik Dahmen is the author of various research papers on hash-based cryptography.

Preface 5
Contents 6
List of Contributors 8
Introduction to post-quantum cryptography 9
1 Is cryptography dead? 9
2 A taste of post-quantum cryptography 14
3 Challenges in post-quantum cryptography 19
4 Comparison to quantum cryptography 21
Quantum computing 23
1 Classical cryptography and quantum computing 23
2 The computational model 27
3 The quantum Fourier transform 30
4 The hidden subgroup problem 33
5 Search algorithms 37
6 Outlook 39
References 40
Hash-based Digital Signature Schemes 43
1 Hash based one-time signature schemes 44
2 Merkle’s tree authentication scheme 48
3 One-time key-pair generation using an PRNG 52
4 Authentication path computation 54
5 Tree chaining 77
6 Distributed signature generation 81
7 Security of the Merkle Signature Scheme 89
References 99
Code-based cryptography 103
1 Introduction 103
2 Cryptosystems 104
3 The security of computing syndromes as one-way function 114
4 Codes and structures 124
5 Practical aspects 135
6 Annex 145
References 149
Lattice-based Cryptography 155
1 Introduction 155
2 Preliminaries 160
3 Finding Short Vectors in Random q-ary Lattices 162
4 Hash Functions 165
5 Public Key Encryption Schemes 173
6 Digital Signature Schemes 188
7 Other Cryptographic Primitives 193
8 Open Questions 194
References 195
Multivariate Public Key Cryptography 201
1 Introduction 201
2 The Basics of Multivariate PKCs 202
3 Examples of Multivariate PKCs 206
4 Basic Constructions and Variations 210
5 Standard Attacks 223
6 The Future 237
References 242
Index 251