I don't think you'd need to resort to another lib.
Godot uses mbedtls internally. It's a third party integration. You can find the mbedtls in thirdparty and under modules.
This is a C crypto library.
I would recommend looking through their documentation.
https://tls.mbed.org
and the source: https://github.com/ARMmbed/mbedtls
The provide example programs you might be able to use to generate a gdnative module for yourself
https://github.com/ARMmbed/mbedtls/tree/development/programs
pkey/rsa_encrypt.c, pkey/rsa_decrypt.c: loads an RSA public/private key and uses it to encrypt/decrypt a short string through the low-level RSA interface.
The string size limitation is artificial but anything larger might require several cipher updates.