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Table of Contents
Intro; Contents; 1 Introduction; 1.1 Homomorphic Encryption in Real Applications: Few Case Studies; 1.2 Summary of This Book; References; 2 Literature Survey; 2.1 FHE in Cloud Computing; 2.2 Mathematical Background; 2.2.1 Somewhat Homomorphic Encryption; 2.3 Few Related Works; 2.4 FHE in Practical Algorithms; 2.5 Conclusion; References; 3 Sorting on Encrypted Data; 3.1 FHE Comparison Based Sort; 3.1.1 Homomorphic Form of Sorting; 3.2 Sorting and Security; 3.2.1 The CPA Indistinguishability Experiment; 3.2.2 Why Comparison Based Sorting is Secured?
3.3 Partition Based Sorting with Index Encryption3.3.1 Encrypted Array with Encrypted Index; 3.3.2 Problems of Recursion on Encrypted Data; 3.3.3 Quick Sort Using Encrypted Stack; 3.3.4 Encrypted Quick Sort Implementation; 3.4 Timing Requirement for Sorting Schemes on Encrypted Data; 3.4.1 Performance Analysis of Different Operations; 3.4.2 Further Reduction of Recrypt to Introduce Error; 3.4.3 Encrypted Insertion Sort; 3.5 Conclusion; References; 4 Translating Algorithms to Handle Fully Homomorphic Encrypted Data; 4.1 Challenges of Executing Encrypted Programs
4.2 Encrypted Variants of Basic Operators4.3 Encrypted Bitwise and Assignment Operators; 4.4 Encrypted Arithmetic Operators; 4.4.1 Encrypted Addition and Subtraction; 4.4.2 Encrypted Multiplication; 4.4.3 Encrypted Division; 4.5 Encrypted Relational Operators; 4.5.1 Encrypted Comparison Operation; 4.5.2 Encrypted Less Than/Greater Than Operator (FHE_Grt and FHE_Less); 4.6 Loop Handling on Encrypted Operations; 4.7 Encrypted Program Termination Using Interrupt; 4.8 Recursion Handling with Encrypted Operations; 4.8.1 Design of Encrypted Stack; 4.9 Design of Encrypted Queue
4.10 Design of Encrypted Linked List4.11 Conclusion; References; 5 Secure Database Handling; 5.1 Security Issues in Cloud; 5.2 Sate of the Art; 5.3 Basic Operations for Database Handling and Their Encrypted Variants; 5.3.1 INSERT and SELECT Operation; 5.3.2 TOP; 5.3.3 LIKE; 5.3.4 ORDER BY; 5.3.5 GROUP BY; 5.4 Advanced SQL: Encrypted JOIN; 5.5 SQL Injection on Encrypted Database; 5.6 Conclusion; References; 6 FURISC: FHE Encrypted URISC Design; 6.1 Existing Encrypted Processors; 6.1.1 Heroic: Partial Homomorphic Encrypted Processor
6.2 Implementing Fully Homomorphic Encrypted Processor Using a Ultimate RISC Instruction6.2.1 Justification of Encrypted Processor Along with Encrypted Data; 6.2.2 Why URISC Architecture in Connection to FHE; 6.2.3 Performance Based Challenge; 6.3 Design Basics of FURISC; 6.3.1 Design of FURISC; 6.3.2 Encrypted Memory Module; 6.3.3 Encrypted ALU Module; 6.3.4 Overall Architecture; 6.4 Comparison with MOVE Based URISC; 6.4.1 Performance Evaluation: SBN Versus Move FURISC; 6.5 FURISC Applied to Realize Encrypted Programs; 6.6 Results; 6.6.1 Drawback of FURISc
3.3 Partition Based Sorting with Index Encryption3.3.1 Encrypted Array with Encrypted Index; 3.3.2 Problems of Recursion on Encrypted Data; 3.3.3 Quick Sort Using Encrypted Stack; 3.3.4 Encrypted Quick Sort Implementation; 3.4 Timing Requirement for Sorting Schemes on Encrypted Data; 3.4.1 Performance Analysis of Different Operations; 3.4.2 Further Reduction of Recrypt to Introduce Error; 3.4.3 Encrypted Insertion Sort; 3.5 Conclusion; References; 4 Translating Algorithms to Handle Fully Homomorphic Encrypted Data; 4.1 Challenges of Executing Encrypted Programs
4.2 Encrypted Variants of Basic Operators4.3 Encrypted Bitwise and Assignment Operators; 4.4 Encrypted Arithmetic Operators; 4.4.1 Encrypted Addition and Subtraction; 4.4.2 Encrypted Multiplication; 4.4.3 Encrypted Division; 4.5 Encrypted Relational Operators; 4.5.1 Encrypted Comparison Operation; 4.5.2 Encrypted Less Than/Greater Than Operator (FHE_Grt and FHE_Less); 4.6 Loop Handling on Encrypted Operations; 4.7 Encrypted Program Termination Using Interrupt; 4.8 Recursion Handling with Encrypted Operations; 4.8.1 Design of Encrypted Stack; 4.9 Design of Encrypted Queue
4.10 Design of Encrypted Linked List4.11 Conclusion; References; 5 Secure Database Handling; 5.1 Security Issues in Cloud; 5.2 Sate of the Art; 5.3 Basic Operations for Database Handling and Their Encrypted Variants; 5.3.1 INSERT and SELECT Operation; 5.3.2 TOP; 5.3.3 LIKE; 5.3.4 ORDER BY; 5.3.5 GROUP BY; 5.4 Advanced SQL: Encrypted JOIN; 5.5 SQL Injection on Encrypted Database; 5.6 Conclusion; References; 6 FURISC: FHE Encrypted URISC Design; 6.1 Existing Encrypted Processors; 6.1.1 Heroic: Partial Homomorphic Encrypted Processor
6.2 Implementing Fully Homomorphic Encrypted Processor Using a Ultimate RISC Instruction6.2.1 Justification of Encrypted Processor Along with Encrypted Data; 6.2.2 Why URISC Architecture in Connection to FHE; 6.2.3 Performance Based Challenge; 6.3 Design Basics of FURISC; 6.3.1 Design of FURISC; 6.3.2 Encrypted Memory Module; 6.3.3 Encrypted ALU Module; 6.3.4 Overall Architecture; 6.4 Comparison with MOVE Based URISC; 6.4.1 Performance Evaluation: SBN Versus Move FURISC; 6.5 FURISC Applied to Realize Encrypted Programs; 6.6 Results; 6.6.1 Drawback of FURISc