Hybrid encryption
Encrypt the data with a fast symmetric key, then encrypt that key with an asymmetric system, so no single algorithm has to do both jobs badly.
Public-key encryption is slow and only handles short messages. Symmetric encryption is fast but needs the two parties to share a key already. Hybrid encryption combines them: a random session key is encrypted to the recipient's public key, and the bulk data is encrypted under the session key. PGP works this way, and TLS does something similar in its key exchange.
Modern theory describes it as a key encapsulation mechanism (KEM) followed by a data encapsulation mechanism (DEM). Failures tend to sit in the glue rather than the primitives. If the session key is not bound to its context, or if the encapsulated key can be modified without detection, you get malleability and padding problems. Use a vetted combination instead of assembling your own.