The message 58 − 0 − 24 − 23

has been encoded from single letter message units using the RSA public

key cryptosystem. The alphabet consists of the ordinary English alphabet

A - Z and the letter b which stands for space. The recipient was foolish to

adopt as his public key: n = 91, e = 59.

Find the secret key and decode the message.

I've worked out d to be 11, with 59d = 1 mod 72.

So using the formula M = C^11 mod 72, I know I have to calculate

and

So calculating the first one in a table...

mod 72

n 58^n

1 58

2 52

4 40

8 16

11 = 58 x 52 x 16 = 48256

I then get 48256 = 16 mod 72 which gives me the letter Q.

But I know that the message should be LATE, so can anyone please explain where I am going wrong?!

Thanks in advance!