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On the Internal Structure of the Advanced Encryption Standard and Two AES-Based Cryptographic Constructions Jianyong Huang University of Wollongong

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University of Wollongong Research Online University of Wollongong Thesis Collection University of Wollongong Thesis Collections 2012 On the internal structure of the advanced encryption standard and two AES-based cryptographic constructions Jianyong Huang University of Wollongong Recommended Citation Huang, Jianyong, On the internal structure of the advanced encryption standard and two AES-based cryptographic constructions, Doctor of Philosophy thesis, School of Computer Science and Software Engineering, University of Wollongong, 2012. http://ro.uow.edu.au/theses/3517 Research Online is the open access institutional repository for the University of Wollongong. For further information contact Manager Repository Services: [email protected]. NIVERSITY U OF WOLLONGONG On the Internal Structure of the Advanced Encryption Standard and Two AES-Based Cryptographic Constructions A thesis submitted in fulfilment of the requirements for the award of the degree Doctor of Philosophy from UNIVERSITY OF WOLLONGONG by Jianyong Huang School of Computer Science and Software Engineering May 2012 c Copyright 2012 by Jianyong Huang All Rights Reserved ii Dedicated to My Family iii Declaration This is to certify that the work reported in this thesis was done by the author, unless specified otherwise, and that no part of it has been submitted in a thesis to any other university or similar institution. Jianyong Huang May 7, 2012 iv Abstract The Advanced Encryption Standard (AES) is a symmetric-key encryption standard adopted by the U.S. government in 2000. It is one of the most popular algorithms used in symmetric key cryptography nowadays. In this thesis, we study the internal structure of the AES algorithm and two AES-based cryptographic primitives: the ALPHA-MAC message authentication code and the LEX stream cipher. In the analysis of the AES internal structure, we focus on two areas: the internal algebraic properties and the key schedule of the AES algorithm. This thesis makes the following four contributions. First, we ask the question what happens if we change the values of some bytes of some intermediate results during an AES encryption. We aim to investigate the impact of these changes on the output of the encryption, and study the feasibility of cancelling out the effects of such changes. By using the structural features of the AES round transformation, we propose a five-round algebraic property which shows that if one carries out four extra exclusive or operations on four fixed-position bytes in some round, five consecutive rounds of such operations will cancel out all changes made to the intermediate results and, consequently, the final output of the encryption will not be affected by these changes. Second, we use the proposed five-round algebraic property of the AES cipher to study the construction of the ALPHA-MAC. We introduce two methods: the Backwards-aNd-Backwards search algorithm and the Backwards-aNd-Forwards search algorithm. By combining these two methods, one can find second preimages of the ALPHA-MAC, given an intermediate value. In addition, we demonstrate that the second-preimage search algorithm can also be used to generate internal collisions for the ALPHA-MAC if an intermediate value is known. Third, we carry out further investigations on the key schedule of the AES cipher, and our research identifies some repeated differential properties in the AES-128 and AES-256 key schedules. In the case of AES-128, if the difference of two secret keys has a special pattern, which we call repeated differential pattern, the propagation of the difference via the key schedule will produce at least seven zero differences in each round, and the same pattern repeats every four rounds. In the case of AES-256, we v show that two secret keys with a double-sized repeated differential pattern generate similar repeated features in the resultant subkeys. Fourth, we describe a differential fault analysis of the LEX stream cipher. The attack exploits computational errors during keystream generation to recover secret keys of the cipher. In our analysis, the cipher is assumed to have random faults in its states and typically, there is one random faulty bit injected during each computation. In the proposed attack, the adversary can extract the secret key of LEX by analysing the output keystream generated by 40 faults. vi Acknowledgements The road to my doctoral degree has been a long but rewarding journey. I would like to thank the following people and organisations. Without their help and support, this thesis would not have been possible. I am grateful to my principal supervisor, Professor Jennifer Seberry, for her guidance and suggestions throughout this thesis. I am especially thankful for her kindness and patience over the past few years. It has been a pleasure to study under her supervision. Her knowledge and academic experience have been invaluable to me. I wish to express my sincere gratitude to my co-supervisor, Professor Willy Susilo, who has supervised me with his knowledge and patience while giving me the freedom to work in my own way. I appreciate all his contributions of time and ideas to make my research experience productive and stimulating. I specially want to thank him for offering many helpful opinions and lots of administrative support. I am thankful to Professor Eli Biham for many fruitful and interesting discussions during his visit to University of Wollongong in 2004. During his three-month stay in Wollongong, I was able to learn how he approached and solved problems, which helped me to develop the capability to carry out independent research. I thank the Centre for Computer and Information Security Research (CCISR) for organising regular research seminars, which gave me the opportunity to hear presenta- tions and to converse with other researchers. I also thank the Research Student Centre for allowing me to take a long leave of absence. I would like to acknowledge the generous financial support of the University Post- graduate Award, funded by University of Wollongong. I thank the School of Computer Science and Software Engineering, and CCISR for sponsoring me to attend research conferences. Finally, I am grateful to Zhen Luo for always being the first person to discuss my undeveloped thoughts with, and for constantly providing support when needed. Last but not least, I would like to thank my parents, Yulan Zhao and Xinmin Huang, for continually encouraging me to complete the doctoral degree. vii Publications During my PhD studies, I have published the following papers. Please note that the contributions of Paper 6 and Paper 7 are not included in this thesis in order to maintain content consistency. 1. Jianyong Huang, Willy Susilo, and Jennifer Seberry. Repeated differential prop- erties of the AES-128 and AES-256 key schedules. In Huaimin Wang, Stephen R. Tate, and Yang Xiang, editors, the 10th IEEE International Conference on Trust, Security and Privacy in Computing and Communications - IEEE TrustCom 2011, Changsha, China, November 16-18, 2011, Proceedings, 2011, to appear. 2. Jianyong Huang, Willy Susilo, and Jennifer Seberry. Differential fault analysis of LEX. In Juan A. Garay and Roberto De Prisco, editors, Security and Cryptog- raphy for Networks, the 7th International Conference, SCN 2010, Amalfi, Italy, September 13-15, 2010, Proceedings, Lecture Notes in Computer Science volume 6280, pages 55-72. Springer, Heidelberg, 2010. 3. Jianyong Huang, Jennifer Seberry, and Willy Susilo. A five-round algebraic prop- erty of AES and its application to the ALPHA-MAC. International Journal of Applied Cryptography (IJACT), volume 1, number 4, pages 264-289, 2009. 4. Jianyong Huang, Jennifer Seberry, and Willy Susilo. A five-round algebraic prop- erty of the Advanced Encryption Standard. In Tzong-Chen Wu, Chin-Laung Lei, Vincent Rijmen, and Der-Tsai Lee, editors, Information Security, the 11th Inter- national Conference, ISC 2008, Taipei, Taiwan, September 15-18, 2008, Proceed- ings, Lecture Notes in Computer Science volume 5222, pages 316-330. Springer, Heidelberg, 2008. 5. Jianyong Huang, Jennifer Seberry, and Willy Susilo. On the internal structure of ALPHA-MAC. In Phong Q. Nguyen, editor, Progress in Cryptology - VI- ETCRYPT 2006, the First International Conference on Cryptology in Vietnam, Hanoi, Vietnam, September 25-28, 2006, Proceedings, Lecture Notes in Com- puter Science volume 4341, pages 271-285. Springer, Heidelberg, 2006. viii 6. Jianyong Huang, Jennifer Seberry, Willy Susilo, and Martin W. Bunder. Secu- rity analysis of Michael: the IEEE 802.11i message integrity code. In Tomoya Enokido, Lu Yan, Bin Xiao, Daeyoung Kim, Yuan-Shun Dai, and Laurence Tian- ruo Yang, editors, Embedded and Ubiquitous Computing - EUC 2005 Workshops, Nagasaki, Japan, December 6-9, 2005, Proceedings, Lecture Notes in Computer Science volume 3823, pages 423-432. Springer, Heidelberg, 2005. 7. Jianyong Huang, Willy Susilo, and Jennifer Seberry. Observations on the mes- sage integrity code in IEEE802.11 wireless LANs. In Tadeusz Wysocki, editor, the 3rd Workshop on the Internet, Telecommunications and Signal Processing - WITSP 2004, Adelaide, Australia, 20-22 December 2004, Proceedings, pages 328- 332, CD-ROM, 2004. ix Contents Abstract v Acknowledgements vii Publications viii 1 Introduction 1 1.1 TheDevelopmentofAES ......................... 3 1.2 MotivationsandObjectives ........................ 3 1.3 Contributions ................................ 5 1.4 ThesisStructure............................... 6 2 A Description of AES 8 2.1 Encryption ................................
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