Office: Armstrong Hall 408H

Office Hours: MW 9:30am-10:30am, Thurs 1pm-2pm, and by appointment

Class Meetings: MW 8:30am-9:20am in Armstrong Hall 117

Homework Workshops: W 5:00pm-6:00pm in Armstrong Hall 119

Text:

No. | Date | Class Summary | Section(s) | Quiz | Quiz Soln | Comments |

1 | Jan 8 | Introduction; Caesar Cipher | 1.1 | - | - | - |

2 | Jan 10 | Substitution Ciphers | 1.{1,2} | Quiz 0 in class; HW1 available. | ||

3 | Jan 13 | Divisibility | 1.2 | - | - | - |

4 | Jan 15 | Greatest Common Divisor; Euclidean Algorithm | 1.2 | - | - | - |

5 | Jan 17 | Algorithm Analysis | 1.2 | Quiz 1 in class; HW2 available. | ||

6 | Jan 22 | Modular Arithmetic I | 1.3 | - | - | Note: HW2 has been modified. |

7 | Jan 24 | Modular Arithmetic II | 1.3 | Quiz 2 in class; HW3 available. | ||

8 | Jan 27 | Group of Units; Caeser Cipher and Modular Arithmetic | 1.3 | - | - | - |

9 | Jan 29 | Fast Powering Algorithm; Primes; Fun. Thm. of Arith. | 1.4 | - | - | - |

10 | Jan 31 | Test 1 in class | 1.{1-3} | HW4 available. | ||

11 | Feb 3 | Order of primes in integers | 1.4 | - | - | - |

12 | Feb 5 | Finite Fields; Modular Exponentiation | 1.{4-5} | - | - | - |

13 | Feb 7 | Fermat's Little Theorem | 1.5 | Quiz 4 in class. | ||

14 | Feb 10 | Applications of FLT; Order of elts. in finite fields | 1.5 | - | - | HW5 available. |

15 | Feb 12 | Primitive Roots | 1.5 | - | - | - |

16 | Feb 14 | History of Cryptography; Formal Cryptosystems | 1.{6-7} | Quiz 5 in class; HW6 available. | ||

17 | Feb 17 | Properties of ciphers | 1.7 | - | - | - |

18 | Feb 19 | Examples: multiplicative cipher; affine cipher | 1.7 | - | - | - |

19 | Feb 21 | Exclusive-or; Pseudorandom generators | 1.7 | Quiz 6 in class; HW7 available. | ||

20 | Feb 24 | Asymetric ciphers; Discrete Logarithm; Diffe-Hellman | 1.7,2.2,2.3 | - | - | HW7 updated. |

21 | Feb 26 | ElGamal 1 | 2.4 | - | - | - |

22 | Feb 28 | Test 2 | 1.4-1.7, 2.2, 2.3 | - | ||

23 | Mar 3 | Snow Day: No Class | - | - | - | - |

24 | Mar 5 | ElGamal vs. Discrete Log Problem | 2.4 | - | - | - |

25 | Mar 7 | Class canceled due to jury duty | - | - | - | No quiz today. |

26 | Mar 17 | Big-Oh notation; algorithm analysis | 2.6 | - | - | HW8 assigned. |

27 | Mar 19 | Shanks's Algorithm for DLP | 2.7 | - | - | - |

28 | Mar 21 | Chinese Remainder Theorem I | 2.8 | Quiz 8 in class | ||

29 | Mar 24 | Chinese Remainder Thm II; Choice of p and g |
2.8,2.9 | - | - | HW9 assigned. |

30 | Mar 26 | Euler's formula for pq |
3.1 | - | - | - |

31 | Mar 28 | Euler's formula for pq |
3.1 | Quiz 9 in class | ||

32 | Mar 31 | Euler's formula for pq; RSA |
3.1,3.2 | - | - | HW10 assigned. |

33 | Apr 2 | RSA; Equivalence of factoring N and computing N' |
3.2 | - | - | - |

34 | Apr 4 | Test 3 | 2.4-3.1 | HW10 due. | ||

35 | Apr 7 | Factoring N vs computing N'; Man-in-the-middle |
3.2, 3.3 | - | - | HW11 assigned. |

36 | Apr 9 | Other Implementation Concerns | 3.3 | - | - | - |

37 | Apr 11 | Miller--Rabin Primality Testing I | 3.4 | HW11 due; Quiz 11 in class | ||

38 | Apr 14 | Miller--Rabin Primality Testing II | 3.4 | - | - | - |

39 | Apr 16 | Elliptic Curves | 5.1 | HW12 due; Quiz 12 in class | ||

40 | Apr 21 | Elliptic Curves II | 5.1 | - | - | HW13 assigned. |

41 | Apr 23 | Elliptic Curve Cryptography | 5.2,5.4 | - | - | - |

42 | Apr 25 | Other topics: Quantum Computers, Lattice Based Cryptography, Digital Signatures | - | - | - | HW13 due. |

- | Apr 30 | Final Exam: 11am-1pm | - | - | - | - |

milans@math.wvu.edu