| Week | Date | Topic | Comments | Quiz Dates |
| One | 15 and 17 January | History | Codes and Ciphers: From Queen Mary of Scots to the Navajo Code Talkers of WWII. See lecture notes on Canvas-- this material is not in our textbook. | |
| Two | 22 and 24 January | 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 | For Undergraduates Only: Prerequisite Assessment Quiz Due on Monday by 11:59pm (almost midnight). The quiz is online and can be found on canvas under Course Summary. |
| Three | 29 and 31 Jan | 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 | 5 and 7 Feb | Beginning of Encyrption Tools | Encryption Schemes, Alphabets and Words, Permutations, Block Ciphers, Simple Example of Stream Cipher, Affine Ciphers. | Quiz 0 due no later than 12:30pm as an upload (one quiz per team) on canvas on Monday: open book, open notes, open friends, open internet. Write up your own solutions together with your team. Do not wait until the last minute to upload your quiz-- no late quizzes will be accepted under any circumstances!!!!!!!!!!! |
| Five | 12 and 14 Feb | Secret Sharing Schemes | Affine and stream ciphers. Secret Sharing Schemes: 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). There is a Mathematica nobebook on Canvas with a secret sharing tutorial in this week's module. | |
| Six | 19 and 21 Feb | 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. 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. | Quiz 1 due no later than 12:30pm as an upload (one quiz per team) on canvas on Monday: open book, open notes, open friends, open internet. Write up your own solutions together with your team. Do not wait until the last minute to upload your quiz-- no late quizzes will be accepted under any circumstances!!!!!!!!!!! |
| Seven | 26 and 28 Feb | 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. | |
| Eight | 4 and 6 March | Midterm March 4 (grad and undergrad) and Project Proposal (grad) March 6 | The Midterm Exam (grad and undergrad) is in class, in person, without your team, on Monday 4 March 12:30-1:45pm in Lawrence Street Center Room 840. You may bring two pages of notes (8.5" x 11") on both sides and calculators are allowed. Do not hand in the notes. | |
| Nine | 11 and 13 March | AES | Guest speakers: Dalton, Michael, and Julian. 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) | |
| null | 18-24 March | Spring Break: no classes, no office hours | < | |
| Ten | 25 and March | Elliptic Curve Cryptosystems-- Chapter 16 (and a few warmups) | 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; | Quiz 2 due no later than 12:30pm as an upload (one quiz per team) on canvas on Monday: open book, open notes, open friends, open internet. Write up your own solutions together with your team. Do not wait until the last minute to upload your quiz-- no late quizzes will be accepted under any circumstances!!!!!!!!!!! |
| Eleven | 1 and 3 April | Flipping Coins and Playing Poker over the phone. Riemann Hypothesis | Tools: Fermat's Little Theorem and Quadratic Residues | |
| Twelve | 8 and 10 April | Guest Lecture; Deception | Video and Slides on Canvas | |
| Thirteen | 15 and 17 April | Art and Math Lecture | Video on Canvas | |
| Fourteen | 22 and 24 April | Grad Student Video Presentations | Various topics; videos will be posted on Canvas | Quiz 3 due no later than 12:30pm as an upload (one quiz per team) on canvas on Monday: open book, open notes, open friends, open internet. Write up your own solutions together with your team. Do not wait until the last minute to upload your quiz-- no late quizzes will be accepted under any circumstances!!!!!!!!!!! | Fifteen | 29 April and 1 May | FINAL EXAM (undergrads only): Monday, April 29th, In person from 12:30-1:45 in Lawrence Street Center Room 840. | Shamir Secret Sharing is the sole topic of the final exam, which you will do as one team-- all undergrads. | FINAL EXAM (undergrads only) WILL BE A JOINT EFFORT: Shamir Secret Sharing Scheme; each of you will be given one share in the scheme and you will, together, discover the secret. Open book, open notes, open software, open friends, open internet. | Sixteen | Week of 6 May | Office hours on Monday to be determined |