Does a passphrase with high entropy provide the same level of security as the private key itself?

General scenario: An attacker has access to a private key file that is protected with a passphrase that has the highest entropy imaginable. Does this provide an advantage to the attacker?

A more concrete scenario: Synology offers a convenient cloud backup service to the users of the NAS systems: C2. It's protected with "AES-256 and RSA-2048 encryption". But: They also upload the private key into the cloud. To me this sounds alarming. But I actually can't judge if this makes any difference when choosing a passphrase with high entropy.

  • $\begingroup$ RSA-2048 provides about 112 bits of security. There's little reason to use something so weak with AES-256. That makes me think the rest of their design is suspect, so I'd question whether they can't actually decrypt the data. $\endgroup$ – SAI Peregrinus Dec 8 '20 at 3:25
  • $\begingroup$ I also think the design is suspect. What do you think is the weakest link here, RSA-2048 or the fact that they deliberately compromise the private key? Apart from this concrete scenario the question of the maximal protection by the passphrase is really interesting to me for crypto in general. $\endgroup$ – schnatterer Dec 8 '20 at 8:41
  • $\begingroup$ Deliberately compromising the private key. But RSA-2048 + AES-256 (what mode? no mention is also suspect) is weird. RSA-2048 + AES-128 would be fine. RSA-4096 + AES-256 would be fine. Assuming RSA-KEM or RSA-OAEP to encrypt the secret key. Not mentioning that is suspect. $\endgroup$ – SAI Peregrinus Dec 8 '20 at 14:21
  • $\begingroup$ I'm also unclear on how they're using RSA. Are they encrypting the AES key which encrypts the backups? Then there's no need to bother with RSA if there's a passphrase anyway, it adds an extra step and reduces the effective security to 112 bits. $\endgroup$ – SAI Peregrinus Dec 8 '20 at 14:35

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