Glitch_in_the_Crypt_Exploiting_Faulty_RSA_Decryption

A high-security server, SecureVault Inc., uses RSA encryption to protect sensitive data. The server utilizes a 1024-bit RSA key and employs the CRT optimization during decryption to improve performance.

Due to a hardware fault, the server occasionally introduces errors during the decryption process. Specifically, the fault affects the computation of m_p = c^{d_p} mod p during the CRT step, causing m_p to be incorrect, while m_q = c^{d_q} mod q remains correct.

As an experienced cryptanalyst, you have managed to obtain access to the server's decryption service. Your goal is to exploit the faulty decryption results to recover the prime factors p and q of the RSA modulus n, effectively breaking the encryption scheme and recovering the private key.