Announcements: Homework 1 coming Monday…

1. DTTF/NB479: Dszquphsbqiz Day 8 • Announcements: • Homework 1 coming Monday… • Practical quiz during week 4 on putting your code to work • Questions? • Today: • Wrap up LFSR ciphers • Substitution, Playfair, and ADFGX ciphers

2. LFSR Demo • Determine key length by computing determinants • Use the key length to solve for the recurrence. • Verify your solution by using the solution to generate the whole key

3. Substitution ciphers • Each letter in the alphabet is replaced by another one. • Which ciphers have we seen are substitution ciphers? • Which aren’t and why? • Breaking ciphertext only uses linguistic structure. Frequencies of: • Single letters • Digrams (2-letter combinations) • Trigrams • Where do T&W get their rules like “80% of letters preceding n are vowels”? (p. 26) • See http://keithbriggs.info/documents/english_latin.pdf • Lots of trial and error when done by hand. • Could automate with a dictionary.

4. Playfair ciphers • Matrix-based block cipher used in WWI • In a 5x5 matrix, write the letters of the word “playfair” (for example) without dups, and fill in with other letters of the alphabet, except I,J used interchangeably.

5. Playfair encryption • Break plaintext into letter pairs • If a pair would contain double letters, split with x • Pad end with x • hellothere becomes… • he lx lo th er ex • For each pair, • If they are in the same row, replace each with the letter to its right (mod 5) • he  KG • If they are in the same column, replace each with the letter below it (mod 5) • lo  RV • Otherwise, replace each with letter we’d get if we swapped their column indices • lx YV He lx lo th er ex KG YV RV QM GI KU To decrypt, just reverse!

6. Weaknesses • P is unknown, but structure of its bottom is predictable • Can break using digram frequencies • Example: If a digram and its reverse both appear often, it’s probably ER and RE. • Each plaintext letter maps to how many possible ciphertext letters? He lx lo th er ex KG YV RV QM GI KU

7. Playfair ciphers • Used in Dorothy L. Sayers’ 1932 mystery novel Have His Carcase • Marketing beats technology? • Invented by Charles Wheatstone • Lyon Playfair, a Scottish Baron, promoted it • Who got the glory?

8. ADFGX ciphers • Why ADFGX? • Morse code for these are very different • Combined cryptography with error-correction • Matrix 1: • 25 letters (i and j merged again) randomly placed • Each plaintext letter replaced by its row and column labels • hello there  • XA FA AA AA FF DG XA FA DF FA

9. ADFGX ciphers (2) • XA FA AA AA FF DG XA FA DF FA • Matrix 2: pick a random keyword and write the previous result under it in scanline order. • Shuffle the columns into alphabetical order • Then read down the columns

10. ADFGX ciphers (3) • XA FA AA AA DG FF XA FA DF FA • Matrix 2: pick a random keyword and write the previous result under it in scanline order. • Shuffle the columns into alphabetical order • Then read down the columns to get ciphertext: • XAXFAFAAAAAADDAGFFFF

11. ADFGX Decryption easy… • …if you know the original matrix and the keyword. • Example? • Read about decryption ideas in text • Variation: ADFGVX cipher allows 26 letters + 10 digits