Amazon EC$2$ uses RSA to encrypt and decrypt login information. Which of the following statements about RSA are true?

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

RSA builds its security on the fast modular exponentiation.

RSA is secure if the size of the modulo is large enough.

In RSA key generation, a user can choose any integer as his encryption key.

In RSA, the private key of a user depends on his public key.

RSA can be used as a digital signature scheme.