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How to complete this proof of statistically indistinguishable distributions?

I'm not sure whether this answers your question, but here is a proof that it should be computationally infeasible to show a statistical distance between the two distributions for a preimage resistant ...
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Vector commitments using only symmetric cryptography

A simple method for an $n$-long vector $v$ is to select $n$ random secret keys $k_i$ for $i=0,\ldots n-1$. Now compute an HMAC for each key-component pair i.e. $H_i:=\mathrm{HMAC}(k_i,v_i)$, sort the ...
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