Homework 2 -- Due Jan 23

- Read the handout "Cracking the Enigma" and note several points of interest
for discussion next class.
- Using a 2x2 Hill cipher with key k, plaintext RACECBRS (I know, that's
not a word) becomes
ciphertext HGWSNXJC.
- 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.

- -x refers to the additive inverse of x
- Encrypt the message "HELLO" using k.
- (Extra credit) I originally used the plaintext RACECARS. Why did I change it to RACECBRS?

- Determine k. You may need to brush up on your linear algebra, and
remember that all arithmetic is mod 26. This means that: