Calendar
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- 4/16/2025 – We briefly reviewed polynomial long division for the assignment. Then we talked about uses of Fermat and Euler’s theorems for encryption. We also looked at the Chinese Remainder Theorem which allows us to solve systems of equations and to carry out calculations using smaller numbers and then stitch them back together. Don’t forget that the exam is next week.
- 4/9/2025 – We reviewed the Perfect Secrecy slides we had looked at before. This finished of the on class content for chapters 4 and 5, be sure to read the chapter content. We also agreed to move the Chapter 4-5 exam to 4/23/2025. We then started looking at the math that we need for chapters 6, 7, & 8. Specifically we looked at fast exponentiation, Fermat’s Little Theorem, Euler’s \(\phi\)-Function, and Euler’s Theorem.
- 4/2/2025 – We reviewed the Feistel Cipher and then looked at DES and AES. We finished by looking at some of the background abstract math related to the Addition and Multiplication of Bytes in the AES algorithm.
- 3/26/2025 – Exam on Chapters 1, 2, & 3
- 3/12/2025 – We went through the slides covering the material from chapter 4. The slides on Feistel’s cipher have been updated: Feistel, DES, and AES (Updated 3/12/2025)
- 3/5/2025 – We covered the basics of transposition ciphers and discussed representing permutations as matrices. You should read through chapter 3. We agreed to move the Unit 1 Exam to after break, remember that it covers content from chapters 1 through 3 along with the material listed below.
- 2/26/2025 – Today we practiced cracking polyalphabetic ciphers using the techniques we last week. We also tried looking at using the techniques discussed in section 2.6 but ran into technical difficulties; I’ll try to get that sorted before next week. Next week we will go over material from chapter 3. In the meantime you should finish reading chapter 2.
- 2/12 & 2/19 – At this point we have covered all of chapter 1 and the first five sections of chapter 2. We will pick up with material from the rest of chapter 2 next week.
- 2/5/2025 – We covered Frequency Analysis this week and next week we will look at Hill’s Cipher. Here is a link to the analysis tools we used: Analysis Tools, and here are some encryption/decryption tools: Encryption Tools.
- 1/29/2025 – Today we discussed modular arithmetic, multiplicative and additive identities and inverses, greatest common divisors, the Euclidean Algorithm, Bezout’s Lemma, multiplicative and affine encryption, and briefly introduced decryption. Next week we will focus on frequency analysis, you should read section 1.5, pp.18-19. You could also take a look at section 1.6, we will start that if there is time.
- 1/22/2025 – We looked at a broad overview of the history of cryptology from Caesar (50BCE) to the present. We also discussed briefly the terms cryptology, cryptography, steganography, code, cipher, transposition, and substitution. For next week you should complete reading sections 1.1-1.4 (pp.1-17)
Unit 1: Basic Ciphers
Assignment:
Exam Guide:
- Readings: Chapters 1-3
- Vocabulary:
- Chapter 1: Cryptology, Cryptography, Steganography, Cryptanalysis, Code, Ciper, Transposition, Substitution, Plaintext, Ciphertext, Key, Kerckhoffs’ Principle, Modular equivalence, Additive Inverse, Multiplicative Inverse, Zero Divisors, Greatest Common Divisor (gcd), Relatively Prime, Division Algorithm, Euclidean Algorithm, Prime Numbers, Prime Factors/Factors, Monoalphabetic, Polyalphabetic, Polygraphic, Determinant, Known-Plaintext, Ciphertext-Only, Additive Cipher, Multiplicative Cipher, Affine Cipher, Hill’s Cipher, Atbash
- Chapter 2: Index of Coincidence, Probability, Frequency, Least common Multiple (lcm), Vigenere, Alberti, Jefferson, Enigma/Rotor Ciphers
- Chapter 3: Scytale, Transposition Cipher, Keyed Columnar Transposition, Route Cipher, Permutation, Functions, Expansion Function, Compression Function, One-to-One (1-1), Onto, Commutative, Mean, Variance, Binomial distribution, Contact Method, Anagraming, Conditional/Compound Probabilities, Logs
Unit 2: Ciphers in the 20th Century
Assignment:
Exam Guide:
- Readings: Chapters 4 & 5
- Skills:
- Given a corresponding diagram you should be able to explain:
- Explain the One-Time Pad cipher
- Explain roughly why the One-Time Pad cipher offers perfect secrecy
- Explain Autokey Ciphers
- Carry out basic polynomial arithmetic modulo 2, i.e.\[(x^3+x+1)+(x+1)\equiv x^3\pmod{2}\] or \[(x^3+x+1)\times(x+1)\equiv x^4+x^3+x^2+1\pmod{2}.\]
Unit 3: Mathematical Ciphers and Public-Key Cryptography
Assignment:
Exam Guide:
- Readings: Chapters 6-8
- Vocabulary: Fermat’s Little Theorem, Euler’s \(\phi\)-Function, Euler’s Theorem, Greatest Common Divisor, Relatively Prime, RSA, Diffie-Hellman, ElGamal, …
- Skills: Fast exponentiation, Finding values of Euler’s \(\phi\)-Function, Using Fermat’s Little Theorem to test for primality, Using Euler’s or Fermat’s theorem to simplify exponentiation, …
Misc. Links and Handouts
