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"public shared data" $\:$ = $\:$ the ordered pair whose entries are [a key for a full-domain statistically injective PRF] and [a signature verification key] $\hspace{.04 in}f$ is an arbitrary one-way function. For each positive integer $j$, [$o_j$ is the value of the PRF at $j\hspace{.03 in}$] and [$i_j$ is [[the signature for $o_j$] concatenated with ...

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