IMPROVED DISTRIBUTED LEDGER TRANSACTIONS WITH HOMOMORPHIC COMPUTATIONS by HANES BARBOSA MARQUES DE OLIVEIRA B.S., Universidade Potiguar, Brazil, 2009 A thesis submitted to the Graduate Faculty of the University of Colorado Colorado Springs in partial fulfillment of the requirements for the degree of Master of Science Department of Computer Science 2020 © Copyright by Hanes Barbosa Marques de Oliveira 2020 All Rights Reserved This thesis for the Master of Science degree by Hanes Barbosa Marques de Oliveira has been approved for the Department of Computer Science by Edward C. Chow, Chair Carlos Paz de Araujo Philip N. Brown 3 December 2020 Date ii Barbosa Marques de Oliveira, Hanes (M.S., Computer Science) Improved Distributed Ledger Transactions with Homomorphic Computations Thesis directed by Professor Edward C. Chow ABSTRACT This thesis proposes a model to protect and transfer data ownership securely, driven by Homomorphic Encryption (HE) primitives and protocols applied to private blockchain technologies. Regarding Blockchain-as-a-Service (BaaS), our contribution seeks to alleviate issues such as third-party custody of digital assets, opportunism, and other adversarial issues. We addressed a recurrent challenge in a Distributed Ledger Technology (DLT) by adapting a HE to the inherent blockchain principles. Both blockchain and HE technologies suffer from performance issues, and the combination of these tools can escalate the issue. Therefore, we apply Clifford Algebra as the algebraic structure for devising an efficient solution. We show the relationships between each aspect of the proposed model, the architecture and related principles, along with the concepts and values expected for a BaaS environment. Our prototype performs well with larger keys, where the system demonstrated a linear performance when keys ranged from 128 to 4096 bits, in operations such as encryption, the addition of ciphertexts, and decryption. Although the key generation procedure showed exponential behavior on keys greater than 2048 bits, symmetric schemes such as the one analyzed can apply lower security parameters than asymmetric constructions, staying inside of the performance range of distributed ledgers. iii DEDICATION This work is dedicated to a very distinct group of individuals called family, my great booster in all of my efforts. To my wife and sons that I love with all my heart. To my beloved parents, my brother, and my sister. I know I am always in your prayers. To “vovó” and all my family abroad, always rooting for me. May God bless your heart! iv ACKNOWLEDGEMENTS First and foremost, I thank the world’s architect and most prestigious scientist, the Almighty God, Who gave me breath. What an unspeakable privilege! I am grateful for the life of Dr. Carlos Paz de Araujo, a visionary not just for the greatness in the astonishing things but also for the perception of the hidden treasures in the small ones. I also express my gratitude to Greg Jones for his encouragement in moments where his support was paramount. To Dr. Edward C. Chow, for sharing his expertise in the guidance of this research. Also, my appreciation for the insights of distinguished professors, Dr. Jonathan Ventura, Dr. Sang-Yoon Chang, and Dr. Philip N. Brown. To Ben Westrich, for his enlightenment on economics. I want to express my special gratitude to David Honorio, my brother in arms in a journey full of challenges. David proposed the cryptographic scheme for this work, accepting my suggestions on how to mold the construction into a blockchain suited proposition. Also, to Marcelo Xavier, Bryan Sosa, Bhagiradh Kantheti, and Jordan Pattee, a distinct breed of partners. Finally, my appreciation to all my family, colleagues, and professors that somehow helped in this achievement by pouring their advice and knowledge over me. v Table of Contents CHAPTER 1 Introduction 1 1.1 The Beginning of Blockchain . 3 1.1.1 The Ideological Design of Bitcoin . 4 1.1.2 Blockchain Fundamental Properties . 5 1.2 Challenges in the Opportunity . 6 1.2.1 Trust Rooted Problems . 7 1.2.2 Custody of Data and Property of Information . 7 1.3 Relevant Solutions . 8 1.3.1 Cryptography as a Common Factor . 9 1.3.2 Private Blockchains . 10 1.4 Our Contribution . 11 1.4.1 Objectives . 14 1.4.2 Organization . 15 1.4.3 Methodology . 16 2 Related Work 19 2.1 Bitcoin: the Blockchain Seminal Work . 21 2.1.1 Transactions and Scripts . 23 2.1.2 Mining Blocks for Consensus . 26 2.1.3 The Economic Vocation of Blockchain . 31 2.1.3.1 Opportunism and Adversarial Problems . 32 2.1.3.2 Property and Ownership . 32 2.2 Distributed Systems . 33 2.2.1 What is a Distributed System? . 34 vi 2.2.2 Fault Tolerance . 36 2.2.3 Byzantine Agreement . 39 2.2.4 Consensus . 41 2.3 Permissioned Blockchains . 44 2.4 Blockchain as a Service . 45 2.4.1 Old Problems for new Chains . 46 2.4.2 The Ownership Management . 48 2.4.2.1 Information as the Data Asset . 50 2.4.3 BaaS Adversarial Problem . 51 2.5 Promising Candidates . 53 2.5.1 Homomorphic Encryption as a Tool . 55 2.5.2 Geometric Algebra as the Catalyst . 56 3 Theoretical Analysis and Discussion 58 3.1 Theorizing a Solution . 59 3.1.1 Contractual Solutions . 59 3.1.2 Renegotiation Mechanism . 61 3.1.3 Ownership Transfer . 61 3.2 A Theoretical Cryptographic Model . 63 3.2.1 The Encryption Scheme . 63 3.2.2 A Protocol For Exchanging Keys . 66 3.2.3 Transferring Ownership by Key Update . 67 3.3 Summary of Our Contribution . 68 4 Research Results and Propositions 71 4.1 Applied Objects and Operations . 71 4.2 Blockchain Framework . 73 4.3 Cryptographic Scheme . 74 4.3.1 Key Generation . 75 4.3.2 Encryption . 75 4.3.3 Addition . 77 vii 4.3.4 Scalar Division . 77 4.3.5 Decryption . 78 4.4 Key Exchange Protocol . 79 4.5 Key Update Protocol . 82 4.5.1 Token Generation . 82 4.5.2 Key Update . 83 4.6 Conclusion . 84 5 Software Architecture of SCOT 86 5.1 System Development . 87 5.1.1 Use Case Scenario . 87 5.1.2 Requirement Analysis . 88 5.1.3 System Constraints . 89 5.2 SCOT System Design . 90 5.2.1 SCOT Architecture View . 91 5.2.2 Why a CLI Prototype? . 93 5.2.3 The Application Lifecycle . 94 5.2.3.1 Persisting Information . 94 5.2.3.2 Generating a Report . 95 5.2.3.3 Generating a Result . 96 5.3 Application . 97 5.3.1 Prototype Execution . 99 5.3.2 Inserting Sensitive Data Into The Blockchain . 99 5.3.3 Creating Analysis Over Third-Party Data . 102 5.3.4 The Ownership Transfer . 103 5.3.5 Analyzing the Information Transferred . 105 6 Performance Evaluation of SCOT 107 6.0.1 Key Generation . 108 6.0.2 Encryption . 109 6.0.3 Addition . 110 viii 6.0.4 Decryption . 111 6.1 Experience Outline . 112 7 Lessons Learnt 114 7.1 A Chain of Events . 115 7.2 Misleading Conceptions . 116 7.3 Analytical Benchmarking . 117 7.3.1 Generated Artifacts . 118 7.4 Development Challenges . 120 8 Future Directions 122 9 Conclusion 123 Bibliography 125 APPENDIX A Setup And Configuration Guides 141 A.1 Prerequisites . 141 A.1.1 Git . 141 A.1.2 Fabric Samples Repository . 141 A.1.3 Golang . 142 A.1.4 Docker And Docker Compose . 142 A.2 Setup . 142 A.2.1 Preparing The Smart Contract . 144 A.2.2 Installing And Instantiating The Smart Contract . 144 ix List of Tables TABLE 6.1 Bit lengths for different SCOT security levels. 107 6.2 Bit lengths for different security levels. ..