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Cryptography is concerned with the conceptualization, definition and construction of computing systems that address security concerns. This book presents a rigorous and systematic treatment of the foundational issues: defining cryptographic tasks and solving new cryptographic problems using existing tools. It focuses on the basic mathematical tools: computational difficulty (one-way functions), pseudorandomness and zero-knowledge proofs. Rather than describing ad-hoc approaches, this book emphasizes the clarification of fundamental concepts and the demonstration of the feasibility of solving cryptographic problems. It is suitable for use in a graduate course on cryptography and as a reference book for experts.
Main Topics covered by the work
Background on Probability and Computation
Motivation to the Rigorous Treatment
Computational Difficulty (One-Way Functions)
Motivation and Definitions
One-Way functions: Weak implies Strong
Variants and advanced material
Hard-Core Predicates
Pseudorandom Generators
Motivation and Definitions
Constructions based on One-Way Permutations
Pseudorandom Functions
Advanced material
Zero-Knowledge Proofs
Motivation and Definitions
Zero-Knowledge Proofs for NP
Advanced material
Appendixs
Brief Background on Computational Number Theory
Brief Outline of Volume 2
Bibliography and Index