| Week | Date | Current Events | Topic | Comments | Assignments |
| Week One | 21 and 23 August 2018 | E. Gethner | History of Codes and Ciphers, From Queen Mary of Scots to the Navajo Code Talkers of WWII | Class Notes | |
| Two | 28 and 30 August 2018 | Background Number Theory | Hierarchy of numbers; formal definition of division; divisors and proper divisors; prime numbers; GCD (You should review the Euclidean and Extended Euclidean Algorithm on your own in Ch 1); relatively prime numbers; Euler's Phi function; modular arithmetic; equivalence relation | Hw 0 handed out in class on 28 August and Quiz 0 is on 11 September. | |
| Three | 4 and 6 September | Group Theory, Fermat's Little Theorem | Equivlance relations revisited; examples of Groups both finite and infinite; order of an element in a group; order of a group; Theorem 2.9.2; order of a subgroup of a group (Theorem 2.10.9); Grand Finale: proof of Fermat's Little Theorem (needed for RSA later on) | ||
| Four | 11 and 13 September 2018 | Beginning of Encyrption Tools/ Quiz 0 on Tuesday | Encryption Schemes, Alphabets and Words, Permutations, Block Ciphers, Simple Example of Stream Cipher, Affine Ciphers. | HW 1 coming soon | |
| Five | 18 and 20 September 2018 | Secret Sharing Schemes | Leftover from last time: affine and stream ciphers. For today: start Secret Sharing Schemes; this material is not in our book, but you should read and review basic properties of square matrices (See review of determinants ). The main scheme we will cover is the Threshold Scheme (two different approaches). | ||
| Six | 25 and 27 September 2018 | DES: Selections from Chapter 4 in our textbook. | History of DES; Encryption process; Decryption; Expander function; S-boxes and their output; Key; the function f that takes the modified key and part of the text as input; mulitple Rounds of DES; Present-day lack of Security in DES, which led to the new Encryption Standard, namely AES. Warmup for AES: the mathematics of Fields: Galois Fields, particularly the one of order 256 and its relation to the irreducible polynomial x^8 + x^4 + x^3 + x + 1 with coefficients from the field Z_2. | ||
| Seven | 2 and 4 October 2018 | AES | Guest speaker: Bille Roche. Multiple Key Lengths; 10 Rounds; Input/Output sizes; ByteSubTransformation (non-linear); ShiftRow Transformation (diffuses bits over multiple rounds); MixColumn Transformation (same purpose as ShiftRow); AddRoundKey (XOR this key with the output of the previous layer) | ||
| Eight | 9 and 11 October | Public Key Cryptography and RSA (Chapter 6) | Global Procedure (a high level view of RSA); tranlsation of plaintext to a numerical message; Encryption process [public key=(n,e)]; Decryption process [private key=(p,q,d)]; False proof of correctness; True Proof of correctness; Digital Signature; Discussion of the security of RSA and its history | Project proposal due on October 9th. | |
| Nine | 16 and 18 October 2018 | Quantum Cryptography and the breakage of RSA | Peter Shor's 1994 quantum algorithm that led to the breakage of RSA on any classical computer: that is, integer factorization can be done in polynomial time. | ||
| Ten | 23 and 25 October 2018 | Elliptic Curve Cryptosystems-- Chapter 16 (and a few warmps) | Finite Fields (again); Discrete Log Problem; ElGammal Cryptosystem; Elliptic Curve Cryptosystems; Elliptic Curves mod N; Representing Plaintext on an elliptic curve; Factoring integers using elliptic curves; An Elliptic Curve ElGammal Cryptosystem; | ||
| Eleven | 30 October and 1 November 2018 | Flipping Coins and Playing Poker over the phone | Tools: Fermat's Little Theorem and Quadratic Residues | ||
| Twelve | 6 and 8 November 2018 | To be determined | |||
| Thirteen | 13 and 15 November 2018 | Project Presentations | |||
| Fourteen | 19-23 November 2018 | Thanksgiving Break | |||
| Fifteen | 27 and 29 November | Project Presentations | Sixteen | Office hours on Monday to be determined |