TMA4155 – exercise 1

a. Encrypt wedidit using the Caesar (shift) cipher with key 6.

b. Decrypt WJUPEIA. The text was encrypted using the Caesar cipher with key 22.

c. Encrypt doitnow using the affine cipher with key \((5,3)\).

d. Decrypt EBBURUDA. The text was encrypted using the affine cipher with key \((15,4)\).

a. The text YQQFYQMFRUHQ was encrypted using a Caesar cipher. Find the key and plaintext.

b. The text OZZRIBQZIHZRLQVJSVI was encrypted using an affine cipher. The sender has the bad habit of beginning every message with the word to (followed by the recipient). What is the key?

a. What is the greatest common divisor \(d\) of \(72\) and \(84\)? Determine integers \(x\) and \(y\) so that \(72x+84y=d\).

b. Do the same for the numbers \(728\), \(126\).

c. Use the fact that \(10^k\equiv(-1)^k\pmod{11}\) to determine the remainder of \(123456789\) divided by \(11\).