I'm looking for a Delphi implementation of an asymmetric encryption algorithm without any dependencies on external DLLs. Is there any available?
My goal is to encrypt/decrypt a string (or array of bytes) using a public/private key pair.
SecureBlackBox from Eldos offers a native, comprehensive solution - including certificate management and access to external crypto devices (i.e. USB tokens)
You can try Lockbox - http://sourceforge.net/projects/tplockbox/. It's free and includes RSA among others (Blowfish, MD5, SHA-1, DES, triple-DES, Rijndael, & digital signing of messages).
It comes complete with a good RSA example that demonstrates how to generate your public/private keys and how to actually encrypt and decrypt data using the keys.
I'm currently using it with Delphi 2010.
I realize that the original question stated "no external DLLs" but in the absence of an acceptable answer maybe you should take a look at the OpenSSL DLLs along with this Delphi link which contains an import unit for the library and some good examples on how to use it, including RSA encryption.
I have tinkered with this and got it working pretty well. There are some changes required to make it work with unicode Delphi - but these are mostly to do with changing PChar to PAnsiChar or PBytes.
Simple Delphi wrappers now allow me to sign/verify/encrypt sym or asym and use SSL. And let's be honest - the distribution of the OpenSSL DLLs is a lot more straightforward than some of the Microsoft offerings. Plus it's free and well maintained.
Take a look at the FGInt package on this site: http://submanifold.be/
If you can stomach using Windows services, there is the Crypto API: http://msdn.microsoft.com/en-us/library/aa380255(v=VS.85).aspx
If you are targeting Vista and up, there is the new Cryptography API: Next Generation. This also supports Elliptic Curve crypto: http://msdn.microsoft.com/en-us/library/aa376210(VS.85).aspx
Another very good fairly complete package is the Delphi Encryption Compendium (DEC) 5.2. You can download (Free with source) from http://www.torry.net/pages.php?id=519#939342.