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Crucially, the server never sees (\phi(B_i)) or (s_i'). Instead, the client sends a : [ \pi_i = \textZKP (s_i', \phi(B_i)) : Rep(\phi(B_i), pub) = s_i' \land \textVerify(s_i', C) = 1 ] The server verifies (\pi_i) in milliseconds without learning any biometric data.