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For example, prover sends P = xG and verifier somehow sends back P = xH without learning x. Yes; if the verify knows that $H = yG$, he just computes $P' = yP = xyG = xH$


I think not, because the two types of error correction are doing fundamentally different things. Conventional error correction schemes, for instance Reed-Solomon codes, expect the value to be near some codeword. To correct an erroneous value, they change it to the nearest codeword. You can picture it as a space where some points in the space correspond ...


I'm not sure where Bloom filters necessarily come in. The "standard" way to use additively homomorphic encryption (that's what Paillier is) for set intersection is the oblivious polynomial evaluation (OPE) technique. It works like this: Alice generates a polynomial whose roots are the items in her set: $p(x) = \prod_{a \in A} (x-a)$. She encrypts the ...

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