Why implement if there is allready JCA APIs?
http://docs.oracle.com/javase/7/docs/technotes/guides/security/crypto/CryptoSpec.html
It covers Java Security standards, has plenty of implemented algorithms.
See also some examples:
http://www.flexiprovider.de/examples/ExampleRSA.html
Single Asymmetric Key
RSA java example Encryption / Decryption