to get highest performance Which asymmetric cipher provide fastest encryption/decryption ? ECC or DH ? what key size is recommended today ?
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I prefer a ~128 bit security level. With ECC this means a curve with ~256 bits, with DH or RSA this corresponds to around 3000 bits. If you can accept a lower security level, the advantage of ECC over DH/RSA gets smaller.
My favourite is Curve25519, which has easily available high performance implementations. An alternative is P256 which is a NIST standard, but a bit slower. There are also some other curves/implementations which are faster than Curve25519, but those seem more academic.