Week | Lecture Notes | Topics |
---|---|---|

1 | Redundancy and Information Theory (.pdf - file of slides) | Hamming Error Correction, Entropy, Markov Processes, Redundancy |

2a | Classical Cryptology (.pdf - file of slides) | Concealment, Russian Nihilist, Bacon's Bi-Literal Cipher, Transposition Substitution (Monoalphabetic, Polyalphabetic) |

2b | Classical Cryptology cont.(.pdf - file of slides) | Hill Cipher, Cryptanalysis of a Monoalphabetic Substitution, Friedman (Kappa) Test Cryptomachines, Enigma, One-Time Pad, Kerckhoff's Principle |

3 | Linear Feedback Shift Registers (.pdf - file of slides) | Pseudo-Random Sequences, Feedback Shift Registers, LFSR's, PN-sequences, Linear Equivalence Minimal Characteristic Polynomials, Non-linear functions, Jennings Multiplexing Algorithm |

4 | Data Encryption Standard (DES) Advanced Encryption Standard (AES) (.pdf - file of slides) | The DES Algorithm, Weaknesses of DES, Modes of Operation, Message Authentication Rijndael, GF(256), AES algorithm, Decrypting Rijndael |

5-7 | Public Key Cryptosystems (.pdf - file of slides) | Difficulties with Private Keys, Public Keys, Trapdoor Functions, Signature Schemes |

5a | RSA (.pdf - file of slides) | RSA Algorithm, Euler's function, Practical Considerations, Breaking RSA, PGP |

5a | The extended Euclidean Algorithm (.pdf - file of slides) | Division, Euclidean Algorithm, Extended Euclidean Algorithm, Inverses mod n, Example |

5b | The Solovay-Strassen Primality Test (.pdf - file of slides) | Quadratic residues, Legendre symbol, Jacobi symbol, Pseudo-Primes Solovay-Strassen Algorithm |

6a |
Protocol Failure (.pdf - file of slides) | Square and Multiply, Dictionary Attacks, Common Modulus Problem, Other Failures |

6b | Knapsack Problems (.pdf - file of slides) | Subset Sum Problem, Super Increasing Sets, Merkle-Hellman Cryptosystem, Security |

7 | Finite Fields
(.pdf - file of slides) | Characteristic, Splitting fields, Constructing fields, Finding Irreducible Polynomials GF(8), GF(9), Subfields, Automorphisms of fields |

8 | Factoring (.pdf - file of slides) | Trial Division, Fermat Factoring, p-1 factoring, factor base algorithms, Quadratic Sieve RSA Challenge Numbers |

9a |
Discrete Logarithm Problem (.pdf - file of slides) | Diffie-Hellman Key Exchange, Man in the Middle Attack, El-Gamal's Cryptosystem Shank's Algorithm, Pohlig-Hellman Algorithm |

9b | The Chinese Remainder Theorem (.pdf - file of slides) | The algorithm, example |

9b | Example of the Pohlig-Hellman Algorithm (.pdf - file of slides) | Example |

10 | Digital
Signatures (.pdf - file of slides) | RSA Signatures, El-Gamal Signature Scheme, Hash Functions, Birthday Attacks Digital Signature Standard |

11 |
Coding Theory I Coding Theory II Coding Theory III (.pdf - file of slides) | Linear Codes, Hamming Codes, Syndrome Decoding |

12a | McEliece
Cryptosystem (.pdf - file of slides) | The cryptosystem, example, drawbacks, security, Goppa Codes |

12b | Intro to Projective Geometry (.pdf - file of slides) | Vector spaces, Projective Geometries, Coordinates, Hyperplanes, Ovals, Conics, Knots |

13 | Secret
Sharing Schemes (.pdf - file of slides) | Shamir's Threshold Scheme, Geometric Schemes, Multilevel Schemes, Bank example |

14 | Elliptic Curve
Schemes (.pdf - file of slides) | Forms, Addition Law, Even Characteristic, Hasse's Theorem, Elliptic Curve Cryptosystem Discrete Logs, Representing Plaintext, El-Gamal Digital Signature Scheme, Factoring |

15 | Current Events(.pdf - file of slides) | Topics vary |

16a | Identification Schemes(.pdf - file of slides) | |

16b | Authentication Codes(.pdf - file of slides) |