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CERIAS Tech Report 2007-20 DYNAMIC CRYPTOGRAPHIC HASH FUNCTIONS by William Speirs Center for Education and Research in Information Assurance and Security, Purdue University, West Lafayette, IN 47907-2086 DYNAMIC CRYPTOGRAPHIC HASH FUNCTIONS A Thesis Submitted to the Faculty of Purdue University by William Robert Speirs II In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy May 2007 Purdue University West Lafayette, Indiana ii To my parents, Jeffrey and Ellen iii ACKNOWLEDGMENTS First and foremost I would like to thank my adviser, Samuel S. Wagstaff, Jr. His advice, guidance, and patience helped me to gain a deeper understanding of the field of cryptography and research in general. I would also like to thank only one of my committee members Eugene Spafford for supporting me and my efforts to complete this Ph.D. A special thanks to Bart Preneel (Katholieke Universiteit Leuven) for providing early ideas and agreeing to be part of my preliminary examination committee. I would also like to thank Moses Liskov (The College of William and Mary) for providing me with valuable insight and comments towards the end of my work. Thanks to The Center for Education and Research in Information Assurance and Security (CERIAS) and the Computer Science faculty and staff of Purdue University for providing me with all the necessary resources and an environment that allowed me to complete this work. A special thanks goes to the Pikewerks Corporation and the Air Force Research Laboratory for providing me with funding to accomplish additional research not directly related to this dissertation. Finally, I would like to thank my family and friends. My family has always shown me unconditional support through sometimes tumultuous periods and always encouraged me to pursue this degree. My friends always supported me and endured my sometimes negative discourse about this dissertation. A special thanks goes to my roommates Barry Wittman and Armand Navabi who were always there to humor my ideas and help me especially in those final trying weeks; stick with it guys. \This thesis is dedicated to all the professors that wanted to see me fail, to all the companies that supported me while I was trying to make some money to support my daughter, and all the graduate students in the strug- gle." { Christopher George Latore Wallace (modified) iv TABLE OF CONTENTS Page LIST OF TABLES : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : viii LIST OF FIGURES : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : ix ABBREVIATIONS : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : x ABSTRACT : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : xi 1 Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1 1.1 A Brief History of Cryptographic Hash Functions : : : : : : : : : : : 1 1.2 Current Applications of Cryptographic Hash Functions : : : : : : : : 3 1.3 Motivation for Dynamic Hash Functions : : : : : : : : : : : : : : : : 5 1.4 Scope of This Dissertation : : : : : : : : : : : : : : : : : : : : : : : : 6 1.4.1 Message Authentication Codes : : : : : : : : : : : : : : : : : : 7 1.5 Contributions of This Dissertation : : : : : : : : : : : : : : : : : : : : 8 1.6 Organization of This Dissertation : : : : : : : : : : : : : : : : : : : : 9 1.7 Notation : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 10 2 Traditional Cryptographic Hash Functions : : : : : : : : : : : : : : : : : : 13 2.1 Function Families : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 15 2.2 Adversarial Model : : : : : : : : : : : : : : : : : : : : : : : : : : : : 16 2.3 Methods for Defining Security Properties : : : : : : : : : : : : : : : : 17 2.3.1 Experiment Descriptions : : : : : : : : : : : : : : : : : : : : : 18 2.3.2 The Fixed and Asymptotic Frameworks : : : : : : : : : : : : : 19 2.4 Formal Definitions of Security Properties : : : : : : : : : : : : : : : : 20 2.4.1 Preimage Resistance : : : : : : : : : : : : : : : : : : : : : : : 20 2.4.2 Second Preimage Resistance : : : : : : : : : : : : : : : : : : : 21 2.4.3 Collision Resistance : : : : : : : : : : : : : : : : : : : : : : : : 22 2.5 Notions of Security : : : : : : : : : : : : : : : : : : : : : : : : : : : : 23 v Page 2.5.1 Preimage Resistance : : : : : : : : : : : : : : : : : : : : : : : 24 2.5.2 Second Preimage Resistance : : : : : : : : : : : : : : : : : : : 26 2.5.3 Collision Resistance : : : : : : : : : : : : : : : : : : : : : : : : 27 2.5.4 Implications Between Notions of Security : : : : : : : : : : : : 27 3 Dynamic Cryptographic Hash Functions : : : : : : : : : : : : : : : : : : : 29 3.1 Background and Introduction : : : : : : : : : : : : : : : : : : : : : : 29 3.2 Definition of a Dynamic Cryptographic Hash Function : : : : : : : : 30 3.3 Traditional Properties for Dynamic Hash Functions : : : : : : : : : : 32 3.4 Dynamic Versions of the Traditional Properties : : : : : : : : : : : : 35 3.5 Properties Without Traditional Analogs : : : : : : : : : : : : : : : : 40 3.5.1 Security Parameter Collision Resistance : : : : : : : : : : : : 41 3.5.2 Digest Resistance : : : : : : : : : : : : : : : : : : : : : : : : : 42 3.6 Implications Between Security Properties : : : : : : : : : : : : : : : : 44 3.7 Notions of Security : : : : : : : : : : : : : : : : : : : : : : : : : : : : 49 3.7.1 Implications Between Notions of Security : : : : : : : : : : : : 52 3.8 Using Dynamic Hash Functions in Practice : : : : : : : : : : : : : : : 54 3.8.1 Expected Security for an Ideal Dynamic Hash Function : : : : 54 3.8.2 Choosing the Right Security Parameter : : : : : : : : : : : : : 56 4 Cryptographic Hash Function Constructions : : : : : : : : : : : : : : : : : 58 4.1 The Merkle-Damg˚ard Construction : : : : : : : : : : : : : : : : : : : 59 4.1.1 Proofs for Preimage Resistance and Collision Resistance : : : 60 4.2 Attacks Against the Merkle-Damg˚ard Construction : : : : : : : : : : 63 4.2.1 The Birthday Attack : : : : : : : : : : : : : : : : : : : : : : : 64 4.2.2 The Length Extension Attack : : : : : : : : : : : : : : : : : : 65 4.2.3 The Multi-Collision Attack : : : : : : : : : : : : : : : : : : : : 65 4.2.4 Herding Attack : : : : : : : : : : : : : : : : : : : : : : : : : : 68 4.2.5 Long Message Second Preimage Attack : : : : : : : : : : : : : 70 4.2.6 Fixed Point Attack : : : : : : : : : : : : : : : : : : : : : : : : 72 vi Page 4.3 New Constructions : : : : : : : : : : : : : : : : : : : : : : : : : : : : 73 4.3.1 The Wide-Pipe Hash and Double-Pipe Hash : : : : : : : : : : 73 4.3.2 Prefix-Free Merkle-Damg˚ard : : : : : : : : : : : : : : : : : : : 76 4.3.3 Enveloped Merkle-Damg˚ard : : : : : : : : : : : : : : : : : : : 78 4.3.4 The Hash Iterative Framework : : : : : : : : : : : : : : : : : : 79 4.3.5 Randomized Hashing: RMX : : : : : : : : : : : : : : : : : : : 82 4.3.6 3C and 3C-X : : : : : : : : : : : : : : : : : : : : : : : : : : : 83 5 A Dynamic Hash Function Construction : : : : : : : : : : : : : : : : : : : 87 5.1 Construction Description : : : : : : : : : : : : : : : : : : : : : : : : : 88 5.1.1 Initial Value Creation : : : : : : : : : : : : : : : : : : : : : : : 90 5.1.2 Message Processing : : : : : : : : : : : : : : : : : : : : : : : : 90 5.1.3 Message Padding : : : : : : : : : : : : : : : : : : : : : : : : : 91 5.1.4 Digest Creation : : : : : : : : : : : : : : : : : : : : : : : : : : 92 5.1.5 Security Parameter Bounds : : : : : : : : : : : : : : : : : : : 93 5.2 The Security of This Construction : : : : : : : : : : : : : : : : : : : : 93 5.2.1 Dynamic Preimage Resistance : : : : : : : : : : : : : : : : : : 97 5.2.2 Dynamic Collision Resistance : : : : : : : : : : : : : : : : : : 100 5.2.3 Security Parameter Collision Resistance : : : : : : : : : : : : 104 5.2.4 Digest Resistance : : : : : : : : : : : : : : : : : : : : : : : : : 105 5.3 Expanding the Digest Size Beyond 4n : : : : : : : : : : : : : : : : : : 106 5.4 Additional Properties : : : : : : : : : : : : : : : : : : : : : : : : : : : 108 5.5 Provisions for Adding Salt : : : : : : : : : : : : : : : : : : : : : : : : 109 5.6 Preventing the Multi-Collision Attack : : : : : : : : : : : : : : : : : : 110 5.7 Implementation Issues : : : : : : : : : : : : : : : : : : : : : : : : : : 111 5.7.1 Speed Comparison : : : : : : : : : : : : : : : : : : : : : : : : 112 6 Summary : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 114 6.1 Conclusion : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 114 6.2 Future Work : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 115 vii Page LIST OF REFERENCES : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 117 A Additional Experiments for Dynamic Hash Function Security Properties : : 124 B Birthday Attacks : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 127 B.1 Preimage : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 127 B.2 Collision : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 128 B.3 k-Collisions : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 129 VITA : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 131 viii LIST OF TABLES Table Page 1.1 Symbols and their description. : : : : : : : : : : : : : : : : : : : : : : 11 1.2 Variables and their description. : : : : : : : : : : : : : : : : : : : : : 12 2.1 The seven notions of security for traditional hash functions. : : : : : 24 5.1 The relative speed of the dynamic hash function construction. : : : : 112 ix LIST OF FIGURES Figure
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    Practical Forward Secure Signatures using Minimal Security Assumptions Vom Fachbereich Informatik der Technischen Universit¨atDarmstadt genehmigte Dissertation zur Erlangung des Grades Doktor rerum naturalium (Dr. rer. nat.) von Dipl.-Inform. Andreas H¨ulsing geboren in Karlsruhe. Referenten: Prof. Dr. Johannes Buchmann Prof. Dr. Tanja Lange Tag der Einreichung: 07. August 2013 Tag der m¨undlichen Pr¨ufung: 23. September 2013 Hochschulkennziffer: D 17 Darmstadt 2013 List of Publications [1] Johannes Buchmann, Erik Dahmen, Sarah Ereth, Andreas H¨ulsing,and Markus R¨uckert. On the security of the Winternitz one-time signature scheme. In A. Ni- taj and D. Pointcheval, editors, Africacrypt 2011, volume 6737 of Lecture Notes in Computer Science, pages 363{378. Springer Berlin / Heidelberg, 2011. Cited on page 17. [2] Johannes Buchmann, Erik Dahmen, and Andreas H¨ulsing.XMSS - a practical forward secure signature scheme based on minimal security assumptions. In Bo- Yin Yang, editor, Post-Quantum Cryptography, volume 7071 of Lecture Notes in Computer Science, pages 117{129. Springer Berlin / Heidelberg, 2011. Cited on pages 41, 73, and 81. [3] Andreas H¨ulsing,Albrecht Petzoldt, Michael Schneider, and Sidi Mohamed El Yousfi Alaoui. Postquantum Signaturverfahren Heute. In Ulrich Waldmann, editor, 22. SIT-Smartcard Workshop 2012, IHK Darmstadt, Feb 2012. Fraun- hofer Verlag Stuttgart. [4] Andreas H¨ulsing,Christoph Busold, and Johannes Buchmann. Forward secure signatures on smart cards. In Lars R. Knudsen and Huapeng Wu, editors, Se- lected Areas in Cryptography, volume 7707 of Lecture Notes in Computer Science, pages 66{80. Springer Berlin Heidelberg, 2013. Cited on pages 63, 73, and 81. [5] Johannes Braun, Andreas H¨ulsing,Alex Wiesmaier, Martin A.G.
  • Broad View of Cryptographic Hash Functions

    Broad View of Cryptographic Hash Functions

    IJCSI International Journal of Computer Science Issues, Vol. 10, Issue 4, No 1, July 2013 ISSN (Print): 1694-0814 | ISSN (Online): 1694-0784 www.IJCSI.org 239 Broad View of Cryptographic Hash Functions 1 2 Mohammad A. AlAhmad , Imad Fakhri Alshaikhli 1 Department of Computer Science, International Islamic University of Malaysia, 53100 Jalan Gombak Kuala Lumpur, Malaysia, 2 Department of Computer Science, International Islamic University of Malaysia, 53100 Jalan Gombak Kuala Lumpur, Malaysia Abstract Cryptographic hash function is a function that takes an arbitrary length as an input and produces a fixed size of an output. The viability of using cryptographic hash function is to verify data integrity and sender identity or source of information. This paper provides a detailed overview of cryptographic hash functions. It includes the properties, classification, constructions, attacks, applications and an overview of a selected dedicated cryptographic hash functions. Keywords-cryptographic hash function, construction, attack, classification, SHA-1, SHA-2, SHA-3. Figure 1. Classification of cryptographic hash function 1. INTRODUCTION CRHF usually deals with longer length hash values. An A cryptographic hash function H is an algorithm that takes an unkeyed hash function is a function for a fixed positive integer n * arbitrary length of message as an input {0, 1} and produce a which has, as a minimum, the following two properties: n fixed length of an output called message digest {0, 1} 1) Compression: h maps an input x of arbitrary finite bit (sometimes called an imprint, digital fingerprint, hash code, hash length, to an output h(x) of fixed bit length n.
  • HCAHF: a New Family of CA-Based Hash Functions

    HCAHF: a New Family of CA-Based Hash Functions

    (IJACSA) International Journal of Advanced Computer Science and Applications, Vol. 10, No. 12, 2019 HCAHF: A New Family of CA-based Hash Functions Anas Sadak1, Fatima Ezzahra Ziani2, Bouchra Echandouri3, Charifa Hanin4, Fouzia Omary5 Faculty of Science, Mohammed V University Rabat, Morocco Abstract—Cryptographic hash functions (CHF) represent a The article is organized as follows: in Section 2, a core cryptographic primitive. They have application in digital background on cellular automata and hash functions is signature and message authentication protocols. Their main included. In Section 3, some related works are presented. building block are Boolean functions. Those functions provide Section 4 details the hashing scheme proposed. In Section 5, pseudo-randomness and sensitivity to the input. They also help the result of the different statistical tests and the cryptographic prevent and lower the risk of attacks targeted at CHF. Cellular properties of cellular automata are provided. Next, in Section 6 automata (CA) are a class of Boolean functions that exhibit good a security analysis is performed. Finally, Section 7 summarizes cryptographic properties and display a chaotic behavior. In this the article. article, a new hash function based on CA is proposed. A description of the algorithm and the security measures to II. BACKGROUND increase the robustness of the construction are presented. A security analysis against generic and dedicated attacks is A. Cryptographic Hash Functions (CHF) included. It shows that the hashing algorithm has good security Cryptographic hash functions with good security properties features and meet the security requirements of a good hashing represent a significant part of cryptography. They are the basis scheme.