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. Language: English