### CPSC 430 Spring 2003

Homework 1

Here is a clarification of the homework. Refer to the copy of p. 37
(from 2nd edition of Stallings) that was distributed in class.
As we discussed in class, using the Hill cipher C = KP, where C (the
ciphertext ) and P (the plaintext) are column vectors of length m and K
(the key) is an m x m matrix. This process is used repeatedly with the
same K to produces blocks of length m of C from blocks of length m of
P. The goal of the work on p. 37 is to find K where m=2, P="friday",
and C="PQCFKY".

For ease of typing I will write matrices in row order, so if M is a 2x2
matrix I would write it as (m11 m12)(m21 m22).

- First verify the calculations at the bottom of the page, which are
all mod 26. Show all work.
- Find the inverse of X where X = (5 17)(8 3) Do not just verify
the inverse that is given.
- Find the product of (9 1)(2 15) and (15 16)(2 5).

- Page 37 concludes with the statement that K = (7 19)(8 3). Verify or
disprove this.

- How can the true K be derived from the K that is given? What is this
relationship called?

- A single change in notation, applied in the appropriate places, will
make the presentation on p. 37 correct (although it will still be
somewhat different from that in the 3rd edition). What is this change,
and where does it
need to be applied? What property of matrix multiplication are you
applying?