Introduction to Cryptology

  • Syllabus
  • Text Book: Cryptology Through History and Inquiry
  • Exam II Applications: Applets to use on Your Exam
  • Exam II Data: Click here to get exam data
  • Class Calendar: This is a calendar of what we actually cover, the calendar of what we plan to cover is on the syllabus.
    1. 1/22/19 – We went over the syllabus and worked through an example of decrypting a message written in a cipher.
    2. 1/25/19 – We covered Alberti/Vigenere’s Polyalphabetic Cipher today.  Be sure to look through section 3.1.
    3. 1/29/19 – We covered Vigenere’s Autokey cipher which is a primitive version of a stream cipher. Be sure to review section 3.3.
    4. 2/1/19 – We went through Falconer’s Transposition cipher which is one of the first, if no the first, example of a keyed columnar transposition cipher.
    5. 2/5/19 – We covered Thomas Jefferson’s use of Vigenere’s cipher and his wheel cipher.
    6. 2/8/19 – We spent the class reviewing ciphers for the exam.  You should understand Alberti’s, Vigenere’s, Falconer’s, and Jefferson’s ciphers.  Also review the vocabulary for the unit.
    7. 2/12/19 – WCSU closed due to snow
    8. 2/19/19 – Group Exam 1
    9. 2/22/19 – We looked at Falconer’s comments on the English language and looked at our own samples of text to confirm what he said.  Tuesday we will use these to try and crack a cipher.
    10. 2/26/19 – We spent the class period deciphering Sample Cipher. This took a long time to do as a group out loud, you want to be able to work through it fairly quickly on your own.
    11. 3/1/19 – Deciphering Transposition Ciphers (Sample Analysis)
    12. 3/5/19 – Deciphering Polyalphabetics (Sample Analysis)
    13. 3/8/19 – Analysis Exam
    14. 3/19/19 – We started discussing modular arithmetic (clock math) and looking at how numbers behave differently.  Be sure to look through the rest of the material on modular arithmetic in Section 6.1 so that we can talk about using it to make a cipher next time.
    15. 3/22/19 – We practiced with modular arithmetic and saw how to use it to create a cipher.  We will briefly wrap this up Tuesday and then move on to Hill’s Cipher.
    16. 3/26/15 – We wrapped up affine ciphers and started on Hill’s.  In particular we covered basic matrix arithmetic and looked at how that can be used to encipher a message.  You should try looking at checkpoints 6.2.7 – 6.2.9 for Friday (Hill’s Cipher Section).
    17. 3/29/19 – We practices Hill’s cipher, learned to invert matrices, and how to decipher Hill’s cipher.  We will practice more next time and discuss carrying out a know plaintext attack on Hill’s Cipher.
    18. 4/2/19 – We saw how to decrypt a Hill’s cipher using a ciphertext only attack.  On Friday we will look at a known plaintext attack.
    19. 4/5/19 – Decrypt Hill’s cipher with a crib
    20. 4/9/19 – Feistel’s Cipher (Handout)
    21. 4/12/19 – Simplified Data Encryption Standard (Handout)
    22. 4/16/19 – We reviewed the Simplified Data Encryption Standard one more time and then started discussing Public Key Cryptography and Asymmetric Ciphers
    23. 4/23/19 – Cleanup and Review
    24. 4/26/19 – Exam 3: Symmetric Ciphers
    25. 4/30/19 – Public Key Cryptology and More Modular Arithmetic:  We further discussed Euler’s \(\phi\)-Function giving three steps to using it:
      1. \(\phi(p)=p-1\) for primes,
      2. \(\phi(p^k)=p^{k-1}(p-1)\) for powers of primes, and
      3. \(\phi(nm)=\phi(n)\phi(m)\) for products of relatively prime numbers.

      Finally we introduced Euler’s Theorem and Fermat’s Little Theorem.

    26. 5/3/19 – RSA Encryption: We looked at why Euler’s Theorem and Fermat’s Theorem were true and how they help us create a cipher.  At the end of class we where looking at an example that didn’t quite work out, I was missing a +1.  The generalization of Euler’s Theorem that I wanted was the following:
      If \(n=pq\), p and q relatively prime, and \(a\) is an integer relatively prime to at least one of the integers \(p\) or \(q\), then \[a^{k\, \phi(n)+1}\equiv a \pmod{n}.\]
    27. 5/7/19 – RSA Encryption Continued
    28. 5/10/19 – PGP and Cleanup (Practice Sheet)
    29. 5/16/19 @ 9am – Exam 4 on RSA and Number Theory
  • Assignments:
    • Unit 1:
      • Assignment 1 – You may print this out and fill it out by hand, but it is a fallible form, so if you could download and open it in Adobe Acrobat Reader to type it up and print it, that would be nice.  Due 2/19/2019
    • Unit 2:
    • Unit 3:
      • Assignment 3a: From the section Up Hill Struggle do #’s 1, 3, 6, 7, 9, 11, and 13.  For the enciphering and deciphering exercises demonstrate that you can do it by hand for three or four the characters then use the apps. Due 4/23/2019
    • Unit 4:
    • Extra Credit:
      • Error Submission Form: This form is for the submission of errors found in the text Cryptology Through History and Inquiry.  You earn 0.25% extra credit for simple typos and 0.5% extra for more substantial mistakes, but only if they haven’t already been submitted.
  • Study Guides:
    • Unit 1: Transpositions, Streams, and Blocks
      • Text Material: Chapter 3
      • Vocabulary (use the glossary): Code, Cipher, Encipher, Decipher, Decrypt, Monoalphabetic, Polyalphabetic, Block Cipher, Stream Cipher, Transposition cipher, Substitution Cipher
    • Unit 2: Cryptanalysis
      • Text Material: Section 2.3, Chapter 4
      • Vocabulary (use the glossary): Decipher, Decrypt, Cryptoanalysis, Frequency Analysis, N-Gram, Prime Number, Monoalphabetic Cipher, Polyalphabetic Cipher, Transposition Cipher,
    • Unit 3: Symmetric Key Cryptography
      • Text Material: Chapter 6, Section 7.3, and
      • Affine Ciphers, Hill’s Cipher, Feistel Cipher, Data Encryption Standard
      • Vocabulary (use the glossary): Polygraphic ciphers, Additive Identity, Additive Inverses, Multiplicative Identity, Multiplicative Inverse (Reciprocal), Matrix, Vector, Modular Equivalence, Bit, Nibble, Byte
    • Unit 4: Public Key Cryptography
      • Material:
        • Find \(\phi(n)\)
        • Raise numbers to large powers modulo n
        • Describe RSA
        • Encipher and decipher using RSA given the keys
        • …
      • Vocabulary: Euler’s \(\phi\)-Function, Relatively Prime, Modular Equivalence, Asymmetric Cipher, Multiplicative Identity, Multiplicative Inverse (Reciprocal), …
  • Links and Handouts: