Definitions

Private Key
A pair of integers known only to one party.

Public Key
A pair of integers provided by the holder of the private key, and known to any who want it.

Plain text
The text to be encrypted

Cypher text
The text after encryption

Plain text attack
Attempting to derive the private key from a known plain text and corresponding cypher text and public key.

Adaptive Chosen Plain text attack
Attempting to derive the private key from a specifically chosen plain text and corresponding cypher text and public key.  Further, after each encryption the attacker can chose a new plain text and repeat.

Brute force attack
Testing all possible private keys to find the actual private key used.