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If something in the Signal protocol looks surprising, then the reason it's there is probably related to key compromise. The main thing to keep in mind is the fact that the "identity keys" are long-term secrets. Suppose Alice has long term key $a^*$ and Bob has long-term key $b^*$, with corresponding public keys $g^{a^*}$ and $g^{b^*}$. They can do ...

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