Goldreich O. Foundations of Cryptography. Vol 1. Basic Tools 2004

Textbook in PDF format

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
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