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Integrity and Privacy in the Cloud: Efficient Algorithms for Secure And Abstract of “Integrity and Privacy in the Cloud: Efficient algorithms for secure and privacy-preserving processing of outsourced data” by Esha Ghosh, Ph.D., Brown University, April 2018. An integral component of the modern computing era is the ability to outsource data and computation to remote cloud service providers or CSPs. The advent of cloud services, however, raises important challenges of in terms of integrity and privacy of data and computation. As soon as users delegate computation to cloud platforms (such as Microsoft Azure or Amazon AWS), concerns related to integrity of the results arise. For example, have all correct inputs been used in the computation? Were all the computation steps applied in the correct order? Have the results been delivered untampered? Moreover, in the face of an alarming number of data breaches and massive surveillance programs around the globe, the privacy of outsourced data is becoming more important than ever. This thesis focuses on designing efficient privacy-preserving and verifiable data processing queries for a rich class of data structures along with prototype implementation and experimental validation. In particular, we focus on the following setting: how can a trusted data owner outsource her data to an untrusted server, such that the server will not be able to cheat while answering queries on the stored data. In other words, we require the server to produce a cryptographic proof for each answer it produces. Moreover, we require the proofs to be privacy-preserving, i.e., they should not leak any information about the data structure or the updates on it besides what can be inferred from the answers. We also consider another dimension of privacy for verifiable outsourced data-processing, namely, encrypting the outsourced data. More concretely, we consider the setting where the data structure is encrypted before outsourcing using a customized encryption scheme that allows the server to compute queries on the encrypted data. Furthermore, the client can efficiently check if the server has correctly computed the answer. In this thesis, we focus on range queries, closest point queries, dictionary queries, set algebraic queries and reachability and shortest path queries on general graphs. Integrity and Privacy in the Cloud: Efficient algorithms for secure and privacy-preserving processing of outsourced data by Esha Ghosh A dissertation submitted in partial fulfillment of the requirements for the Degree of Doctor of Philosophy in the Department of Computer Science at Brown University Providence, Rhode Island April 2018 © Copyright 2018 by Esha Ghosh This dissertation by Esha Ghosh is accepted in its present form by the Department of Computer Science as satisfying the dissertation requirement for the degree of Doctor of Philosophy. Date Roberto Tamassia, Director Recommended to the Graduate Council Date Anna Lysyanskaya, Reader Date Seny Kamara, Reader Approved by the Graduate Council Date Andrew G. Campbell Dean of the Graduate School iii Acknowledgements It is a great pleasure to thank everybody without whose continuous support, this thesis would not have materi- alized. First and foremost, I thank my adviser Roberto Tamassia. Roberto has been a truly supportive adviser, an inspiring mentor and a great role model to me. He has always made himself available for me, be it for research meetings or for ethical advice. Roberto’s kind and graceful advising style and his approach towards inclusiveness and diversity is a great source of inspiration for me. I feel truly honored to be his student. I am very thankful to my committee members Anna Lysyanskaya and Seny Kamara who followed my research closely and have mentored me throughout my Ph.D journey. I had the wonderful opportunity to collaborate with Seny towards the end of my Ph.D. I thank Sorin Istrail and John Savage for following my research from time to time and for their great words of encouragement. My heartfelt thanks to Ugur Cetintemel for his insightful career advice and support. I had the pleasure to collaborate with Michael Goodrich in the earlier half of my PhD. Michael’s enthu- siasm and self-critical approach to research greatly shaped my perspective on research. Olya Ohrimenko has been a wonderful mentor, my internship host (at Microsoft Research) and collaborator on multiple projects. She has been a source of unwavering support throughout these years. I am particularly thankful to the security group at Brown; it is a remarkable place for exchanging ideas and sharing constructive criticism. The CS department at Brown could not have fostered such a great academic environment without tremendous contributions from the TStaff and AStaff members. My sincere thanks to Lauren Clarke, Genie DeGouveia, Donald Johwa, Jesse Polhemus, Dawn Reed, Frank Pari and to all other staff members. I am grateful to all my other collaborators, namely, Christian Cachin, Jan Camenisch, Melissa Chase, Angelo De Caro, Apoorvaa Deshpande, Dario Fiore, Cedric Fournet, Markulf Kohlweiss, Dimitrios Pa- padopoulos, Bryan Parno, Alessandro Sorniotti, Björn, Tackman and Nikos Triandopoulos. My collaboration with them has been a great learning experience. A special thanks to my internship mentors Alessandro and Angelo for hosting me at IBM Zurich. I tremendously enjoyed my time at IBM. Thanks to Roberto and the support from my Microsoft research Dissertation Grant, I also had the opportunity to work with a group of bright undergrad and masters students at Brown, Talley Amir, Nick Cunningham and Harjasleen Mal- vai. I thank Donghoon Chang, Melissa Chase, Jonathan Katz, Satya Lokam, Dahlia Malkhi, Charalampos Papamanthou and Sushmita Ruj for hosting me for short visits during my Ph.D. Thanks to Anubhav, Apoorvaa, Cindy, Elizabeth, Evgenios, Jasper, Krishna, Prannath, Sasha, Yizhen and Zhiyu for being such great friends and for making my stay in Providence so fond. A very special thanks to iv Chaya for always being there, every step of the way and for making New York, home. Sajin has been a tremendous source of strength and support during the final years of my Ph.D. I could not have undertaken this journey, far away from home, if not for the unconditional support of my family. Throughout my life, their love and support has given me the courage to pursue my interests unapologetically and has made me the person I am today. v Contents List of Tables ix List of Figures x 1 Introduction 1 2 Efficient Verifiable Range and Closest Point Queries in Zero-Knowledge 4 2.1 Introduction . .4 2.2 Related Work . .6 2.3 Preliminaries . .8 2.4 Model . 10 2.4.1 Security Properties . 10 2.5 Our Construction . 12 2.5.1 Range Query Construction . 13 2.5.2 Closest Point Query . 15 2.5.3 Complexity Analysis for RQ ............................. 16 2.6 Security Analysis . 17 2.6.1 Proof of Soundness . 17 2.6.2 Proof of Zero-Knowledge . 18 2.7 Experiments on Synthetic Data . 19 2.7.1 Data . 19 2.7.2 Setup Phase . 20 2.7.3 Range Query Phase . 20 2.7.4 Server Storage Cost . 21 2.7.5 Comparison with Ostrovsky et al. [123] . 22 2.7.6 Closest Point Query . 23 2.8 Experiments on Real-World Data . 23 2.8.1 Enron Data . 23 2.8.2 Boston Taxi Data . 24 2.8.3 Performance . 24 vi 2.9 Conclusion . 25 3 Zero-Knowledge Accumulators and Set Operations 26 3.1 Introduction . 26 3.2 Preliminaries . 30 3.3 Zero-Knowledge Universal Accumulators . 34 3.3.1 Security Properties . 38 3.4 A Zero-knowledge accumulator from the q-Strong Bilinear Diffie-Hellman Assumption . 41 3.5 Zero-Knowledge Authenticated Set Collection (ZKASC) . 45 3.5.1 Model . 46 3.5.2 Security Properties . 47 3.6 Zero-Knowledge Authenticated Set Collection Construction . 49 3.6.1 Setup and Update Algorithms . 50 3.6.2 Set Algebra Query and Verify Algorithms . 53 3.6.3 Subset Query . 53 3.6.4 Set Intersection Query . 54 3.6.5 Set Union . 56 3.6.6 Set Difference Query . 58 3.6.7 Efficiency Comparison with the Scheme of [127] . 59 3.6.8 Security Proofs . 60 3.7 Conclusion . 68 4 Efficient and Verifiable Graph Encryption Schemes for Shortest Path Queries 71 4.1 Introduction . 71 4.1.1 Our Techniques and Contributions . 72 4.2 Related work . 73 4.3 Preliminaries . 74 4.3.1 Abstract data types and data structures. 74 4.3.2 Structured Encryption . 75 4.4 Graph Encryption for SPSP Queries . 77 4.4.1 Security . 79 4.5 Achieving security in the malicious model . 84 4.6 Experiments . 85 4.6.1 System specifications, Primitives and Data Sets . 85 4.6.2 Graph Dataset . 85 4.6.3 Setup . 86 4.6.4 Search . 87 4.7 Conclusion . 87 vii 5 Efficient and Verifiable Reachability Queries on General Graphs in Zero-Knowledge 90 5.1 Introduction . 90 5.1.1 Related Work . 91 5.1.2 Our Contribution . 91 5.2 Preliminaries . 92 5.2.1 Unforgeable Signature Scheme . 93 5.2.2 Aggregate Signature Scheme . 93 5.2.3 Commitment Scheme . 94 5.2.4 Zero-Knowledge Authenticated Data Structure . 95 5.2.5 Model . ..
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