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CCA-Security for predicate encryption schemes / M. Sc. Gennadij Liske ; Supervisor: Prof. Dr. rer. nat. Johannes Blömer. Paderborn, 2017
Inhalt
General Introduction
Preliminaries
Cryptographic Primitives
Pseudorandom Functions
One-Way-Functions
Families of Collision-Resistant Hash Function
Predicate-Based Schemes
Predicate Families
PE With Public Index
P-KEM With Public Index
Pair Encoding Schemes
Linearity Properties of Pair Encodings
Normal and Regular Pair Encodings
Three Types of Ciphertext Polynomials
Coefficients Properties of Pair Encodings
Security Notions for Pair Encoding Schemes
Security Definitions for Predicate-Based Schemes
Introduction, Related Work, and Main Contribution
Formalization of Security Properties
SS and IND
Semantic Security Template for PE
Indistinguishability Templates for PE and P-KEM
Attack Scenarios and Additional Restrictions of Adversaries
Relations Between SS-Security and IND-Security for PE
Equivalence of SS and IND for PE
Further Proofs
Subtleties in Security Definitions for PE and P-KEM
Handling of User Secret Keys
Weakness of the OK-security
Weakness of the OU-security
Discussion
When and How to Restrict Challenge Decryption
Valid Adversaries and Security Notions
CCA2-Security Template for P-KEM
Separation Results and Implication Results
Fully CCA-Secure Framework in Composite-Order Groups
Introduction, Related Work, and Main Contribution
Background, Construction and Intuition
Preliminaries
Composite-Order Bilinear Groups
Security Assumptions
CCA Security Definition for P-KEMs
Fully CCA-Secure Framework
Additional Requirements of CCA-Secure Framework
Fully CCA-Secure Framework
Intuition Behind the Consistency Checks
Semi-Functional Algorithms
Security of the Framework and the Extended Proof Technique
Main Theorem and an Overview of the Proof
Security Proof of the CCA-Secure Pair Encoding Framework
On the Distribution of Semi-Functional Components
Supplementary Algorithms
Proof of the Main Theorem
Verifiability for Regular Pair Encoding Schemes
Simplified Construction
Further Proofs
Hardness of Factorization Under Subgroup Decision Assumptions
Fully CCA-Secure Framework in Prime-Order Groups
Introduction and Main Contribution
Background, Construction and Intuition
Preliminaries
Matrices of Group Elements and Computation Rules
General Lemmata
Matrix-DDH Security Assumption
CCA Security Definition for PE
Fully CCA-secure Framework
Normal Algorithms
Semi-Functional Algorithms
Properties of Public Parameters, User Secret Keys, and Ciphertexts
Guarantees of the Verification Checks
Intuition Behind the Construction
Correctness
Further Proofs
Security of the Framework
Main Theorem and an Overview of the Proof
Security Proof for the CCA-Secure Pair Encoding Framework
Main Reduction Steps Regarding CCA-Security
Reduction Steps with Simple Extensions
Final Steps
Conclusion and Future Work
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