Heads-up: Check out Mission #4 and consider how to break up the work appropriately.

Read Trappe & Washington Chapter 3 up through the end of Section 3.6, filling in gaps in your learning (and learning about Euler’s Theorem, which we haven’t done in class). Take notes of anything that is unclear/incomplete for you; discuss these issues with your group, since this week’s mission is about Euler’s Theorem.

Begin/continue doing exercises from Chapter 3 as needed to solidify your understanding. Good ones include: 3.13 exercises 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, for now. Not for turning in, and you may want to spread these out through the week.

Get back to reading The Code Book, i.e. Chapter 3, as time permits.

Mission #2 is due today. We will be continuing basic number theory in class, which is Chapter 3 in Trappe and Washington. We’ll be doing 3.4, 3.5 and 3.6 on Friday and/or Monday.

It will be a written quiz taking the whole period. It will be closed-book. I will provide such things as the Vigenere square, multiplication table mod 26, english letter frequencies, and alphabet-to-number table, if needed.

Topics:

Use the Cryptosystem organizer to study the following cryptosystems (so this means being able to describe things like key space, how to encrypt/decrypt, being able to apply various cryptanalysis techniques). I may ask you to encrypt, decrypt, or cryptanalyse.

Caesar cipher

Scytale (no need for any cryptanalysis techniques beyond exhaustive search, but do know the system)

Substitution cipher (alphabetic substitution)

Vigenere cipher

Affine cipher

Hill cipher

You should be adept at:

modular arithmetic

the notion of invertible element in modular arithmetic, finding inverses by inspection

the notion of an invertible matrix in modular arithmetic

notions of divisibility, primes, prime factorization, gcd, lcm

performing the Euclidean algorithm and using it to find inverses in modular arithmetic (to be covered Friday Sept 2)

Terminology you should be able to explain:

cryptography

coding theory

steganography

plaintext and plaintext space

ciphertext and ciphertext space

key and keyspace

types of cryptanalysis: ciphertext only, known plaintext, chosen plaintext, chosen ciphertext

confusion (property of cryptosystem)

diffusion (property of cryptosystem)

On this quiz we won’t have any proofs, but in future ones, we will.

You should know the broad outlines of the history, but I won’t test you on it.

Reminder that Mission #1 is due today. See you in class.

Note: Today we will cover the Euclidean algorithm and its use in finding inverses in modular arithmetic. This is to be found in Sections 3.1, 3.2, and 3.3 of your text. They are assigned for reading (with no particular due date, but note: you have a quiz on Wednesday after the holiday weekend).

Read Chapter 2.6 and 2.7 (Playfair, ADFGX and Block/Hill)

Make sure you can encrypt and decrypt successfully with all types of ciphers by hand: Caesar, Scytale, Substitution, Vigenere, Affine.

Make sure you have thought through each of the possibilities for cryptanalysis (ciphertext only, known plaintext, chosen plaintext, chosen ciphertext) for these.

In general, you may find some exercises in 2.13 helpful and fun in accomplishing the goals above, and testing your ability. You should begin working through them systematically, using your judgment to skip only something you are very sure you know well. The first 12 are on material we’ve covered so far.