I have a quick question about encrypting with private key.

First background: I have a short piece of data (symmetric encryption
key + some other stuff) encrypted with RSA private key.  Then this
symmetric key is decrypted using the corresponding RSA public
key.  I'm using 2048 bit RSA key created with 'openssl genrsa 2048'.
The private key needs to be always secret, encrypted symmetric
key is basically a unique session key, and public key is more like
"shared secret" distributed to several places but not publicly.

Now I'd like to know how difficult it would be to get the symmetric
key without actually having the public key?

Should I generate or modify the RSA key in some specific way to
make this more difficult?

I'm asking because I could not find definite answer in the web
anywhere on how secure is encryption with private key and
decryption with public key. Everything was just about signing
with private key and verifying with public key, always assuming
that the public key is really public and therefore not saying
anything about how difficult it is to crack the private-key
encrypted data without having the public key.  Since I'm no
cryptography expert, I'm trying to avoid any pitfall here.


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