Symmetric versus asymmetric self encryption I can encrypt my files with a symmetric encryption algorithm like AES, or with an asymmetric encryption algorithm like RSA or ECC (I encrypt my files with my own public key). No communication is involved in this scenario. The latter, which one may call asymmetric self encryption, might seem an unusual choice in situations where a key exchange is not required. However, it still does have some advantages: you don't need to type your passphrase for encryption (you need your public key); it works well with keys stored in a hardware token; also, an attacker apparently needs both to have the public key and brute-force the passphrase to decrypt the data. In GnuPG, these two encryptions are achieved via options gpg -c and gpg -e -r USERNAME.

Considering attacks on the asymmetric encryption, does hiding the public key increase the entropy required for a brute force attack? What information does the public key leak to the attacker?

The standard algorithms for symmetric and asymmetric encryption are AES-256, 4098-bit RSA. The answer to the above question helps compare the security level of these algorithms (in terms of the number of bits that needs to be checked).
called asymmetric self encryption


No, not really, you just made up that term.


  might seem an unusual choice in situations where a key exchange is not required


No it doesn't, although commonly a hybrid cryptography is used, especially for EC based cryptography.


  an attacker apparently needs both to have the public key and brute-force the passphrase to decrypt the data.


Of course not, the attacker requires the encrypted private key and a password to unwrap that key using password based encryption (PBE).




  Considering attacks on the asymmetric encryption, does hiding the public key increase the entropy required for a brute force attack? What information does the public key provide to the attacker?


Possibly, but the scheme should of course be secure even if the public key is known to the attacker. Generally the public key is not considered a secret, and that means schemes, but also the implementations of the public key operations are not protected against leaking the public key.


  The standard algorithms for symmetric and asymmetric encryption are AES-256, 4098-bit RSA. The answer to the above question helps compare the security level of these algorithms.


No, it really doesn't. In some situations asymmetric cryptography may be more secure, even though the key strength of the symmetric encryption is larger than the key strength of asymmetric encryption. However, it is impossible to quantify that advantage, so you cannot talk about a "level".