An Introduction to Cryptology

Inhaltsverzeichnis

• 2. Classical Systems.
• 2.1. Caesar, simple substitutions, Vigenère.
• 2.2. The incidence of coincidences.
• 2.3. Vernam, Playfair, Transpositions, Hagelin, Enigma.
• 3. Shift Register Sequences.
• 3.1. Introduction.
• 3.2. Linear feedback shift registers.
• 3.3. Non-linear algorithms.
• 4. Shannon Theory.
• 5. Huffman Codes.
• 6. Des.
• 7. Public Key Cryptography.
• 8. The Discrete Logarithm Problem.
• 8.1. The discrete logarithm system.
• 8.2. How to take discrete logarithms.
• 9. RSA.
• 9.1. The RSA system.
• 9.2. The Solovay and Strassen primality test.
• 9.3. The Cohen and Lenstra primality test.
• 9.4. The Rabin variant.
• 10. The Mceliece System.
• 11. The Knapsack Problem.
• 11.1. The knapsack system.
• 11.2. The Shamir attack.
• 11.3. The Lagarias and Odlyzko attack.
• 12. Threshold Schemes.
• 13. Other Directions.
• Appendix A. Elementary Number Theory.
• A.1. Introduction.
• A.2. Euclid’s Algorithm.
• A.3. Congruences, Fermat, Euler, Chinese Remainder Theorem.
• A.4. Quadratic residues.
• A.5. Möbius inversion formula, the principle of inclusion and exclusion.
• Appendix B. The Theory of Finite Fields.
• B.1. Groups, rings, ideals and fields.
• B.2. Constructions.
• B.3. The number of irreducible polynomials over IFq.
• B.4. The structure of finite fields.
• References.
• Notations.