Curve25519 is one of the fastest ECC curves; it is not covered by any known patents, The reference implementation is Public Domain software.
The original Curve25519 paper defined it as a Diffie-Hellman (DH) function. Daniel J. Bernstein has since proposed that the name Curve25519 be used for the underlying curve, and the name X25519 for the Diffie-Hellman function.