RSA Challenge Three: RSA Broadcast Attack

The Problem: Given RSA ciphertexts with different moduli but the same low encryption exponent, recover the message.

Since you thwarted Malland's plots with Horridland, Malland enlisted the help of two more allies - Awfulland and Badland. Horridland, Awfulland and and Badland made the mistake of all having the same low encryption exponent, e = 3. Malland sent Horridland, Awfulland and Badland the same message about a plan of attack. You get your hands on all three copies of the message:

Awfulland's message, encrypted as c_A = m³ mod n_A (using Awfulland's modulus n_A),
Badland's message, encrypted as c_B = m³ mod n_B (using Badland's modulus n_B), and
Horridland's message, encrypted as c_H = m³ mod n_H (using Horridland's modulus n_H).

Use the fact that all three emails are encrypted using the same low encryption exponent to figure out what the evil plot is.

For this exercise, use the following values:

Name	Value
Number of ciphertexts:	3
Common public exponent:	3
Ciphertext #1
Modulus #1
Ciphertext #2
Modulus #2
Ciphertext #3
Modulus #3