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HANDBOOK
OF FINANCIAL
CRYPTOGRAPHY
AND SECURITY
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CHAPMAN & HALL/CRC
CRYPTOGRAPHY AND NETWORK SECURITY
Series Editor
Douglas R. Stinson
Published Titles
Jonathan Katz and Yehuda Lindell, Introduction to Modern
Cryptography
Antoine Joux, Algorithmic Cryptanalysis
M. Jason Hinek, Cryptanalysis of RSA and Its Variants
Burton Rosenberg, Handbook of Financial Cryptography and Security
Forthcoming Titles
Maria Isabel Vasco, Spyros Magliveras, and Rainer Steinwandt,
Group Theoretic Cryptography
Shiu-Kai Chin and Susan Beth Older, Access Control, Security and
Trust: A Logical Approach
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Chapman & Hall/CRC
CRYPTOGRAPHY AND NETWORK SECURITY
HANDBOOK
OF FINANCIAL
CRYPTOGRAPHY
AND SECURITY
Edited by
Burton Rosenberg
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Chapman & Hall/CRC
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© 2011 by Taylor and Francis Group, LLC
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Printed in the United States of America on acid-free paper
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About the Editor
Burton Rosenberg received a BS in electrical engineering from the Massachusetts Insti-
tuteofTechnology,Cambridge,MA,anMSincomputersciencefromColumbiaUniversity,
NewYork,andanMAandPhDincomputersciencefromPrincetonUniversity,NewJersey.
He has taught at Dartmouth College, Hanover, NH, and is currently an associate professor
of computer science at the University of Miami, Coral Gables, FL.
He has worked both in academia and industry, including a consultant position at the
Mus´ee National d’Art Moderne in Paris. His PhD is also in the field of computational
geometry.
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List of Contributors
Mauro Barni Margaret Jackson
DipartimentodiIngegneriadell’Informazione Graduate School of Business
Universit`a di Siena RMIT University
Siena, Italy Melbourne, Australia
Mira Belenkiy Markus Jakobsson
Microsoft Research Palo Alto Research Center
Redmond, WA Palo Alto, CA
Felix Brandt
Stefan Katzenbeisser
LFE Theoretische Informatik
Security Engineering Group
Ludwig-Maximillians-Universit¨at Mu¨nchen
Technische Universit¨at Darmstadt
Munich, Germany
Darmstadt, Gemany
Lynne Coventry
Aggelos Kiayias
School of Psychology and Sport Sciences
Department of Informatics and Telecom
Northumbria University
National and Kapodistrian University of
Newcastle, UK
Athens
Athens, Greece
George Danezis
Microsoft Research Cambridge
Sjouke Mauw
Cambridge, UK
Facult´e des Sciences, de
la Technologie et de la Communication
Mohammad Torabi Dashti
Universit´e du Luxembourg
Informationssicherheit/ZISC
Luxembourg
Eidgeno¨ssische Technische Hochschule
Zu¨rich, Switzerland
R´obert P´arhonyi
Inter Access B.V.
Claudia Diaz
Hilversum, The Netherlands
ESAT/COSIC
Katholieke Universiteit Leuven
Leuven, Belgium Serdar Pehlivanoglu
Division of Mathematical Sciences
Carl Ellison Nanyang Technological University
New York Singapore
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Ahmad-Reza Sadeghi Sid Stamm
Department of Electrical Engineering and Mozilla
Information Sciences Mountain View, CA
Ruhr-University Bochum
Bochum, Germany Paul Syverson
U.S. Naval Research Laboratory
Reihaneh Safavi-Naini Washington, D.C.
Department of Computer Science
University of Calgary Michael Szydlo
Calgary, Canada Akamai
Cambridge, MA
Nicholas Paul Sheppard
Christian Wachsmann
Department of Computer Science
Chair for System Security
University of Calgary
Ruhr-University Bochum
Calgary, Canada
Bochum, Germany
Radu Sion
Robin Wilton
Department of Computer Science
Future Identity Ltd.
Stony Brook University
Westbury, UK
Stony Brook, NY
Marianne Winslett
Sean Smith Department of Computer Science
Department of Computer Science University of Illinois
Dartmouth College Urbana, IL
Hanover, NH
Jianying Zhou
Chris Soghoian Institute for Infocomm Research
School of Informatics and Computing Agency for Science, Technology and
Indiana University Bloomington Research
Bloomington, IN Singapore
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Contents
Preface xix
Burton Rosenberg
Cryptography, Commerce, and Culture. . . . . . . . . . . . . . . . . . . . . . . . xix
Overview of Chapters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xx
Required Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi
In Closing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxv
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxv
I Protocols and Theory 1
1 E-Cash 3
Mira Belenkiy
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.1 E-Cash Protocols . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.1.2 Security Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.1.3 Building Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2 Chaum’s E-Cash. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2.1 Overview of the Chaum, Fiat, Naor Construction . . . . . . . . . . 10
1.2.2 Blind Signatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.2.3 CFN E-Cash . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.2.4 Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.2.5 Preventing Alice from Being Framed . . . . . . . . . . . . . . . . . 14
1.2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.3 Security . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.3.1 Privacy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.3.2 Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.3.3 Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.3.4 Exculpability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.4 Brands’ E-Cash . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.4.1 Sigma Protocols and the Discrete Log Representation Problem . . 21
1.4.2 Restrictive Blind Signatures . . . . . . . . . . . . . . . . . . . . . . 23
1.4.3 Detecting Double-Spenders via Secret Sharing . . . . . . . . . . . . 24
1.4.4 Brands’ E-Cash . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
1.4.5 Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
1.4.6 Security . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
1.5 CHL: Compact E-Cash . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
1.5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
1.5.2 Zero-Knowledge Proof of Knowledge . . . . . . . . . . . . . . . . . 29
ix
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