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Suppose user A encrypts some data using his public key and stores the data publicly. Later user A would like to transfer that same data to user B publicly by encrypting it using user B's public key.

What is the best way to verify that the same data was transferred to user B without knowing the data, user A, and user B's private keys?

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  • $\begingroup$ Is it homework? $\endgroup$
    – Ievgeni
    Commented Jun 29, 2021 at 9:21
  • $\begingroup$ no, trying to figure out if this is possible at all and what I should read more about. Would like to create something of this sort on Ethereum so secret data can be transferred securely between people publicly. $\endgroup$
    – Newbie
    Commented Jun 29, 2021 at 9:23
  • $\begingroup$ Question : Is it a deterministic encryption scheme? $\endgroup$
    – Ievgeni
    Commented Jun 29, 2021 at 9:24
  • $\begingroup$ I don't know if this is possible at this point so it's too early to set any boundaries. Would be preferable if it's deterministic though. $\endgroup$
    – Newbie
    Commented Jun 29, 2021 at 9:27
  • $\begingroup$ Other question : Is $A$ authorized to add new data (like ZK-proofs) to help B to make the verification? If yes what are the security constraints? $\endgroup$
    – Ievgeni
    Commented Jun 29, 2021 at 9:33

1 Answer 1

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Zero-knowledge proof seems fit with your goal. $A$ has to prove that it exists $M$ such that $C=Enc(M, pk_A)$, and $C^\prime=Enc(M, pk_B)$. This ZKP can be done without revealing any information about the data $M$ (that's why we call it Zero-Knowledge). For concrete instantiation you can use El Gamal encryption, and Groth-Sahai ZK-proof techniques :

https://en.wikipedia.org/wiki/ElGamal_encryption

https://eprint.iacr.org/2007/155

Notice that you do not need to use private key of $B$ to verify the equality but if it is the contact which verifies, it's probably better.

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