Decipher the ciphertext and recover the message from the following information?

Question

A message is coded numerically using the numbers 1 to 26 relating to each letter in the alphabet.

It is then enciphered using RSA cipher to give the ciphertext (18, 54, 25).

Using repeated squaring decipher the ciphertext and find the message.

R7(m) = m^7 (mod 133)

This what I have done so far,

133 = 7x19 with p = 7 and q = 19

(p-1)(q-1) = 108

The multiplicative of 7 in Z108 is 31.

So using the repeated squaring technique for

R31(18), R(54), R(25)

Is this then right way to go, please show me how to complete this problem?

Answer 1

You pretty much solved everything on your own.

18^31 = 18 mod 133

54^31 = 5 mod 133

25^31 = 4 mod 133

So, your message was RED.