See CCITT X.509 (1).
The solution proposed in [AN96]
to correct the authentication flaw
in the CCITT X.509 (1) one message protocol
is to sign the secret data Ya before it is encrypted.
Requirements
The protocol must ensure the recipient B of the message
that the data Xa and Ya originate from A.
Martín Abadi and Roger Needham.
Prudent engineering practice for cryptographic protocols.
IEEE Transactions on Software Engineering, 22(1):6--15, January
1996.