Amazon CloudFront negotiates HTTPS connections to origins using Elliptic Curve Digital Signature Algorithm $($ECDSA$).$ Which of the following statements about ECDSA are not true?

ECDSA builds its security on the difficulty of big integer factorisation.

ECDSA builds its security on the difficulty of discrete logarithm.

An ECDSA signature contains two integers.

In ECDSA key generation, a user chooses his private key at first and then determines his public key.

Given a message, ECDSA signature on the message is unique.

The size of ECDSA signature is usually larger than that of RSA signature.