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 Euclidean algorithm.

In RSA key generation, given the public key, the Euler theorem is used to compute the private key.

RSA builds its security on the difficulty of discrete logarithm.

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

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

RSA can be used to achieve confidentiality but not authenticity.