What is the original message encrypted using the RSA system with n = 53 * 61 and e = 17 if the encrypted message is 3185 2038 2460 2550

Question

To decrypt, first find the decryption exponent d, which is the inverst of e = 13 modulo 42 * 58.

Please show the answer with great detail so I understand how you got the answer

Answer 1

First we calculate the multiplicative inverse of e = 17 modulo 3120 [= 52*60].  This is our decryption exponent, d.  d = 2753.

Now decrypt the message by calculating, mod 3233 [=53*61], as follows:

3185 ^ 2753 = 1816

2038 ^ 2753 = 2008

2460 ^ 2753 = 1717

2550 ^ 2753 = 411 or 0411 [pad a zero here to make four digits.]

Now the decrypted message is 

18, 16, 20, 8, 17, 17, 4, 11 or S, Q, U, I, R, R, E, L.  [here 0 = A, 1 = B, 2 = C, etc.]

SQUIRREL is the original message.

Hope this helps, and thanks for the question.  It was actually fun.  :)