ADVANCED CRYPTOLOGY (COD2) CTY COURSE SYLLABUS. Week 1. Info sheet, pre-test, Sunday survey, honor codes, computer lab forms, check roster.
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1 ADVANCED CRYPTOLOGY (COD2) CTY COURSE SYLLABUS Week 1 Info sheet, pre-test, Sunday survey, honor codes, computer lab forms, check roster Day 1 Previously in Cryptology : skit Introductions Icebreaker involving modular arithmetic Classroom rules The map of CODE on the board CODE map continued Re: cipher wheels & how to do Caesar and Vigenère on TI with his program WHEEL auto-key encryption worksheet #1 on icebreaker and use of WHEEL, auto-key Reviewing with course pack Review of the Euclidean Algorithm Review of the EEA Multiplicative inverses in mods Day 2 Review of public-key cryptography and authentication Knapsack ciphers 1
2 Motivation of and introduction to matrices Worksheet. Heavy on a knapsack exchange and a problem illustrating why 2 x 2 matrices multiply the way they do. Day 3 More on matrices, up to and including inverses and how to do everything on the calculator. Error-correcting codes. Motivation of the generator matrix. More ECC, writing down the steps and getting the students to do it Permutations: cycle notation, composition, identity, inverses Intro to McEliece encryption, up to definition and calculation of public key F Day three worksheet. McEliece public key encryption Day 4 More McEliece stuff. Fermat skit Factoring vs. primality testing as mathematics problems Fermat Factorization Day 4 Worksheet Day 5 2
3 COD2 Map summary of what we ve learned so far in COD2, and calculator program sharing Computer lab: Looking at multiplication tables and exponent tables and making conjectures and seeing the connection to cryptology More time finishing up the lab Discussion of what was learned in the lab The square-multiply method Sideshow: Intro to probability and statistics applied to crypto, up through basic addition and multiplication rules. (Sunday) Worksheet on mods stuff (bring up primitive roots) Week 2 Day 6 More probability, derangements Cracking codes using statistics the index of coincidence Pollard rho factorization Review of Diffie-Hellman and RSA Work on Simon Singh challenge, worksheet ElGamal encryption Day 7 3
4 The Pollard-(p-1) method of factorization Digital signatures and ElGamal applied thereto Constructing new Enigma machines, worksheet Day 8 Primality testing Permutations and their application to the Enigma Carmichael numbers, the Miller-Rabin Primality Test Euler s Phi function Intro to Enigma rotor recovery problem Study for midterm The midterm exam Review of the midterm Completion of second Enigma unit. Day 9 Completion of second Enigma unit, exercises. Day 10 4
5 M-209: The introduction history, how it works, encrypting/decrypting on paper. elective topics: pseudo-random numbers and authentication challenges? P vs. NP complexity issues in mathematics/crypto? M-209 training video from the 1950 s Special lecture in Adams Auditorium with Number Theory and Math Reasoning classes Week 3 Day 11 Extensive history of science and our understanding of the world Our current understanding of the universe and quantum mechanics Quantum computing Quantum computing demo M-209 more about the mathematics underlying the machine Exercises Day 12 The M-209: encrypting manually, and the protocol for its use. The M-209 crack part I: cribbing Quadratic sieve 5
6 The M-209 crack part II: just beginning Exercises related to the day Day 13 M-209 Crack Part II and III: finding relative settings of pins on rotors and the cage, discussion of finishing off the crack Continued fractions Mathematics needed to understand elliptic curves study for final, work on Simon Singh challenge Elliptic curve cryptology Day 14 Final Exam Part I: cracking the Kryha machine Final Exam Part II: cracking the Kryha machine Post-assessment test given Day 15 6
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