Amazon EC$2$ uses RSA to encrypt and decrypt login information. Which of the following statements about RSA are not true?

RSA builds its security on the extended Euler theorem.

RSA builds its security on the difficulty of discrete logarithm.

In RSA, the private key of a user is independent of his public key.

RSA is secure as long as the size of the private key is large enough.

RSA can be used to achieve confidentiality.

RSA can be used to achieve authenticity.