CPSC 430 Spring 2007
Homework 2 -- Due Jan 23

1. Read the handout "Cracking the Enigma" and note several points of interest for discussion next class.

2. Using a 2x2 Hill cipher with key k, plaintext RACECBRS (I know, that's not a word) becomes ciphertext HGWSNXJC.
   1. Determine k. You may need to brush up on your linear algebra, and remember that all arithmetic is mod 26. This means that:
      • -x refers to the additive inverse of x mod 26, so that x + -x = 0 mod 26. For example, 18 and 8 are additive inverses mod 26 because 18+8=26=0 mod 26.
      • 1/x refers to the multiplicative inverse of x mod 26, so that x*(1/x)=1 mod 26. For example, 5 and 21 are multiplicative inverses mod 26 (1/5=21 and 1/21=5) because 21*5=105=1 mod 26. However, 2 has no multiplicative inverse mod 26, so 1/2 is undefined.
   2. Encrypt the message "HELLO" using k.
   3. (Extra credit) I originally used the plaintext RACECARS. Why did I change it to RACECBRS?