Problems

These are some additional problems to think about. The official homework is at here.

1.

Suppose an affine cipher has key [s,t], meaning we first add s and then multiply by t, all done modulo 26. If [s,t]=[7,11] is used for enciphering, what is the key that deciphers the code?

2.

ASCII code associates characters, numbers and other symbols to 8-bit numbers, meaning a string of 8 0's or 1's giving the binary expansion of a number. For instance, the binary character Control-T is ASCII 20 or 00010100 in binary. Capital A is ASCII 65, or 01000001. There are 2⁸=256 ASCII symbols.

(a)

How many keys are there for additive ciphers on ASCII characters?

(b)

How many keys are there for multiplicative ciphers on ASCII characters? What are they?