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Cryptography at Large

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Cryptography at Large Cryptography at Large Cryptography at Large Gerard Tel Trefw: cryptografie, informatiebeveiliging, digitale handtekening, elektronisch geld c Copyright 2009 Gerard Tel. Alle rechten voorbehouden. Niets uit deze uitgave mag worden verveelvoudigd, opgeslagen in een geautomatiseerd gegevensbestand, of openbaar gemaakt, in enige vorm of op enige wijze, hetzij elektronisch, mechanisch, door fotokopie¨en,opnamen, of enige andere manier, zonder voorafgaande toestemming van de auteur. Voorzover het maken van kopie¨enuit deze uitgave is toegestaan op grond van artikel 16B Auteurswet 1912 jo het Besluit van 20 juni 1974, St.b. 351, zoals gewijzigd bij Besluit van 23 augustus 1985, St.b. 471 en artikel 17 Auteurswet 1912, dient men de daarvoor wettelijk verschuldigde vergoedingen te voldoen aan de Stichting Reprorecht. Voor het overnemen van gedeelte(n) uit deze uitgave in bloemlezingen, readers en andere compilatie- of andere werken (artikel 16 Auteurswet 1912), in welke vorm dan ook, dient men zich tot de auteur te wenden. Ondanks alle aan de samenstelling van dit boek bestede zorg kan noch de redactie, noch de auteur, noch de uitgever aansprakelijkheid aanvaarden voor schade die het gevolg is van enige fout in deze uitgave. Contents Contents v Preface ix 1 Quantum Factorization (Bart Jansen ) 1 1.1 Introduction to quantum mechanics . 1 1.2 Shor's factoring algorithm . 4 1.3 Complexity considerations for cryptography . 8 1.4 Implementations of Shor's algorithm . 9 1.5 The future of quantum computing . 10 2 Diffie-Hellman and Discrete Logarithm Problems (Sori Lee ) 11 2.1 The `problems' . 12 2.2 Reducing the DL problem to the DH problem . 13 2.3 Summary . 18 3 Hash Collisions (Jan Olav Hajduk ) 21 3.1 MD5 . 21 3.2 SHA-1 . 26 3.3 Conclusion . 28 4 RSA Challenges (Eleni Mina ) 29 4.1 Introduction . 29 4.2 RSA Challenges . 31 4.3 Conclusion . 38 5 Representation collisions in Pollard's Rho-Method (Sanne Willems ) 39 5.1 Pollard's Rho-Method . 40 5.2 Representation of z .................................. 41 5.3 Application in Pollard's Rho-Method . 43 5.4 Verification with experiments . 43 5.5 Conclusion . 46 6 Phishing (Geerten Doornenbal ) 47 6.1 Phishing - what is it? . 47 6.2 The term phishing . 47 6.3 Different kinds of phishing . 48 6.4 Why does it work? . 51 v vi Contents 6.5 Economic losses . 51 6.6 Technical solution . 52 7 Biometry (Hannelore van der Burgh ) 55 7.1 System . 55 7.2 Attacks . 57 7.3 Biometric traits . 58 7.4 The matching procedure of fingerprints . 61 7.5 Conclusion . 64 8 Privacy of rfid (Roland Vaandrager ) 65 8.1 Introduction . 65 8.2 Example uses of rfid . 65 8.3 Privacy issues . 66 8.4 Possible solutions . 67 8.5 Conclusion . 71 9 Practical Elliptic Curve Cryptography (Tom Smeets ) 73 9.1 Elliptic Curves introduced . 73 9.2 Curve Parameters . 74 9.3 Standardized Curves . 75 9.4 Fast Curve25519 . 77 9.5 Software using ECC . 78 9.6 Addendum . 79 10 GRAIN an eSTREAM Cipher (Zamarak ) 81 10.1 Introduction . 81 10.2 eSTREAM . 83 10.3 GRAIN . 84 10.4 Summary . 91 10.5 Used resources . 91 11 Advanced Encryption Standard (Anieke Brombacher ) 93 11.1 The beginning of AES . 93 11.2 Description of the standard . 94 11.3 Possible attacks on AES . 97 11.4 Summary and Conclusion . 99 12 Non-malleability (Ren´eKersten ) 101 12.1 Introduction . 101 12.2 DDL-Lite . 102 12.3 Improved definition and algorithm . 104 12.4 Non-malleability in other cryptographic primitives . 109 12.5 Summary . 110 13 Broadcast Encryption (Tamar Christina ) 111 13.1 Introduction . 111 13.2 Encryption Schemes . 112 13.3 Traitor Tracing . 115 13.4 Conclusion . 118 Cryptography at Large vii 14 Receipt-freedom in voting (Pieter van Ede ) 119 14.1 Introduction . 119 14.2 Current voting systems . 121 14.3 Receipt-freedom by Moran and Naor . 122 14.4 Discussion and conclusion . 125 15 Safety of the dutch OV-chipkaart (Marcel van Kooten Niekerk ) 127 15.1 Introduction to the OV-chipkaart . 127 15.2 System architecture of the OV-chipkaart . 128 15.3 Safety of the OV-chipkaart-system . 129 15.4 Safety of the disposable OV-chipkaart . 130 15.5 The anonymous and personal OV-chipkaart . 131 Summary and Conclusions . 135 Bibliography 137 Index 145 viii Contents Preface This reader contains papers, written by students of Utrecht University as part of the Cryp- tography course of Fall 2008. The course treats the theory of Cryptography, underlying many solutions in computer and IT security. The challenge for the students is, to connect this theory to actual security products in their project study. The papers were presented during a symposium on January 29, 2009. For the purpose of the symposium, the presentations were divided into three themes, namely Successful Attacks (Chapters 1 through 6), about systems of which the security was broken, Safe Digital Society (Chapters 7 through 12), about security used in a nation-wide scale to support the economical or democratic infrastructure, and New Systems (Chapters 13 through 16), about new ideas or systems under development. The session chairs during the symposium were Marjan van den Akker, Gerard Vreeswijk, and Marinus Veldhorst. I hope the reader will be a nice souvenir for the speakers and writers, and that it will provide for all others an interesting overview of some computer security topics. Gerard Tel (course teacher), Utrecht, February 2009. ix Chapter 1 Quantum Factorization Written by Bart Jansen. In 1994 the American mathematician Peter Shor [Sho97] published an algorithm for factoring integers in polynomial time. Since the security of cryptosystems such as RSA [Tel08, Section 5.3.3] depends on the assumption that factoring large integers is computationally infeasible, this publication came as quite a shock to physicists and computer scientists alike. Because it has proven to be rather difficult to construct a quantum computer with sufficient \memory" to actually run the algorithm on the large integers that are used as RSA moduli, there is currently no threat to the safety of RSA encryption. This chapter investigates the nature of the algorithm, and evaluates how long RSA will remain safe against quantum computers. We start the chapter by introducing some of the basic concepts of quantum mechanics that are be needed to understand why quantum computers are potentially more powerful than classical computers. This is followed by a description of a probabilistic scheme for factoring integers, first published by Miller in 1974 [Mil75]. Miller's factoring scheme forms the basis of Shor's algorithm. Shor showed that the most critical step, finding the order of an element in a modular group, can be performed in polynomial time on a quantum computer. No poly- nomial algorithm is known for solving this problem on classical computers, which illustrates the computational power of a quantum computer. In the last part of this chapter, we look at the advancements that have been made towards implementing a quantum computer that can execute Shor's algorithm. In the exposition of this subject, a strong distinction has been made between physical and number-theoretical discussions. The text on physics will not contain any equations or formal notation, since it only serves to transfer the ideas behind quantum physics to an unini- tiated audience. The part on the number-theoretic properties of Shor's algorithm will be highly mathematical, since it neatly fits into the mathematical background of the course on cryptography. 1.1 Introduction to quantum mechanics The field of quantum mechanics originated in the 1920's, when bright young minds such as Heisenberg, Schr¨odingerand Bohr began to unify the various ad-hoc theories that existed at that time to explain the \strange" outcomes of some experiments in physics. Several effects 1 2 Quantum Factorization that were observed in the lab simply could not be explained by the classical laws of physics as postulated by Isaac Newton and James Maxwell. Even though classical physics had proven very accurate when dealing with macroscopic systems (calculating the motions of the stars, predicting the orbits of satellites and modeling the trajectory of rockets), it failed to explain the effects that were observed for experiments on a much smaller scale. In particular, some experiments seemed to suggest that light exists in the form of individual particles, while other observations seemed to indicate that light consists of waves. The theory of quantum mechanics was developed to explain this duality of light. In the course of the previous century, the theory started to mature. Important predictions that followed from the theory were later confirmed by experiments, and this predictive power was starting to appeal to scientists. Unfortunately quantum mechanics would often lead to conclusions that were extremely counterintu¨ıtive to our normal way of thinking. As we shall see, quantum mechanics does not give us a deterministic view of the world..
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