There are two obvious ways to break RSA. Indeed, these apply to any public-key cryptosystem. An attacker can either attempt to:

  1. Decrypt a ciphertext without knowledge of the private key.

  2. Determine the private key directly from the public key.

The second attack is more powerful since an attacker who can perform the second attack can then decrypt subsequent ciphertexts. We now consider these two attack strategies.

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