P1363 7.2.2 ECSVDP-DHC ECSVDP-DHC is Elliptic Curve Secret Value Derivation Primitive, Diffie-Hellman version with cofactor multiplication. It is based on the work of [DH76], [Mil86], [Kob87], [LMQ98] and [Kal98a]. This primitive derives a shared secret value from one party's private key and another party's public key, where both have the same set of EC domain parameters. If two parties correctly execute this primitive, they will produce the same output. This primitive can be invoked by a scheme to derive a shared secret key; specifically, it may be used with the schemes ECKAS-DH1 and DL/ECKAS-DH2. It does not assume the validity of the input public key (see also Section 7.2.1).
Note: As stated P1363 compatibility mode with ECDH can be preset, and in this case the implementation doesn't have a ECDH compatibility mode (if you want that just use ECDHBasicAgreement and note they both implement BasicAgreement!).