Key exchange with unilateral authentication (short: unilateral key exchange) is an important primitive in practical security protocols; a prime example is the widely deployed TLS protocol, which is usually run in this mode. Unilateral key-exchange protocols are employed in a client-server setting where only the server has a certified public key. The client is then authenticated by sending credentials via a connection that is secured with the key obtained from the protocol. Somewhat surprisingly and despite its importance in practical scenarios, this type of key exchange has received relatively little attention in the cryptographic literature compared to the type with mutual authentication.