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The HMQV protocol has 2 "identity" fields $\hat{A}, \hat{B}$ that are used in the dual signature - and it tries to guarantee that any properly-generated session key is only shared by a single $(A, B, \hat{A}, \hat{B})$ 4-tuple.

However, the paper isn't particularly clear whether a party can use multiple, potentially attacker-controlled, identities.

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