23. Your opponent uses RSA with n = pq and encryption exponent e and encrypts a message m. This yields the ciphertext c ≡ m^e (mod n). A spy tells you that, for this message, m^12345 ≡ 1 (mod n). Describe how to determine m. Note that you do not know p, q, φ(n), or the secret decryption exponent d. However, you should find a decryption exponent that works for this particular ciphertext. Moreover, explain carefully why your decryption works (your explanation must include how the spy's information is used).