Unknown Key-Share (UKS) resilience is a basic security attribute in authenticated key agreement protocols. In this paper we revisit the definitions of this attribute and the method of proving this attribute under the Bellare-Rogaway (BR) model in the literature. We propose a new type of UKS attack, which coerces two entities A and B into sharing a key with each other but in fact A thinks that he is sharing the key with another entity C and B thinks that he is sharing the key with another entity D, where C and D might or might not be the same entity. We call this attack a Bilateral Unknown Key-Share (BUKS) attack. We demonstrate that a few well-known authenticated key agreement protocols are vulnerable to this attack. We then explore a gap between the conventional BR-type proof and a BUKS adversary's behavior, and extend the BR model to cover the BUKS resilience attribute. At the end of the paper, we provide a general countermeasure and its security proof under the extended model and the assumption that a collision-resistance function exists.