Fundamentals of Cryptology

Download fundamentals cryptography pdf tutorial, a complete and free training document under 603 pages by Henk C.A. van Tilborg.

Cryptography is one of the cryptology disciplines dedicated to protecting messages (ensuring confidentiality and / or authenticity) that two people wish to share through an insecure channel, often with the help of secrets or keys.

The history of cryptography is already long. We report its use in Egypt 4,000 years ago. However, for centuries, the methods used had often remained very primitive. On the other hand, its implementation was limited to the needs of the army and diplomacy. Thus, the methods of encryption and cryptanalysis (the code case) experienced a very important development during the Second World War and had a profound influence on the course of it.

Table of contents

• Introduction 
• Introduction and Terminology 
• Classical Cryptosystems 
• Simple Substitution 
• The System and its Main Weakness 
• Cryptanalysis by The Method of a Probable Word 
• The Playfair Cipher 
• Transposition Ciphers 
• Shift Register Sequences 
• Pseudo-Random Sequences 
• Linear Feedback Shift Registers 
• Non-Linear Algorithms 
• Minimal Characteristic Polynomial 
• The Berlekamp-Massey Algorithm 
• A Few Observations about Non-Linear Algorithms 
• Problems 
• Block Ciphers 
• An Identity Verification Protocol 
• Triple DES 
• Shannon Theory 
• Entropy, Redundancy, and Unicity Distance 
• Mutual Information and Unconditionally Secure Systems 
• ElGamal's Secrecy System 
• ElGamal's Signature Scheme 
• Further Variations 
• Digital Signature Standard 
• Schnorr's Signature Scheme 
• The Nyberg-Rueppel Signature Scheme 
• How to Take Discrete Logarithms 
• An Example of the Pohlig-Hellman Algorithm 
• RSA Based Systems 
• The RSA System 
• Some Mathematics 
• Setting Up the System 
• A Factorization Algorithm for a Special Class of Integers 
• A Small Secret Exponent; Wiener's Attack 
• Some Physical Attacks 
• Timing Attack 
• The 'Microwave' Attack 
• How to Generate Large Prime Numbers; Some Primality Tests 
• Trying Random Numbers 
• Decryption 
• Precomputation 
• Finding a Square Root Modulo a Prime Number 
• The Four Solutions 
• How to Distinguish Between the Solutions 
• The Equivalence of Breaking Rabin's Scheme and Factoring n 
• Problems 
• Elliptic Curves Based Systems 
• Some Basic Facts of Elliptic Curves 
• The Geometry of Elliptic Curves 
• A Line Through Two Distinct Points 
• A Tangent Line 
• Addition of Points on Elliptic Curves 
• Cryptosystems Defined over Elliptic Curves 
• The Discrete Logarithm Problem over Elliptic Curves 
• The Discrete Logarithm System over Elliptic Curves 
• The Security of Discrete Logarithm Based EC Systems 
• Problems 
• Coding Theory Based Systems 
• Introduction to Goppa codes 
• The McEliece Cryptosystem 
• The System 
• Setting Up the System 
• Encryption 
• Decryption 
• Discussion 
• Problems 
• Hash Codes & Authentication Techniques 
• Introduction 
• Problems 
• Secret Sharing Systems 
• Introduction 
• Threshold Schemes 
• Threshold Schemes with Liars 
• Secret Sharing Schemes 
• Visual Secret Sharing Schemes 
• Problems 
• A Elementary Number Theory 
• Introduction 
• Euclid's Algorithm 
• Congruences, Fermat, Euler, Chinese Remainder Theorem 
• The Structure of Finite Fields 
• The Cyclic Structure of a Finite Field 
• The Cardinality of a Finite Field 

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