verifying that a private key can decrypt a payload in multi key encryption

amlwwalker

6/26/24, 6:01 PM

If Bob takes a plaintext and encrypts it with their own public key and hands it to Eve who in turn encrypts it with her public key, we now have a cipher text that requires both Bob and Eve to decrypt it, to get the original plaintext. However once Eve has encrypted it, is there anything Bob can do to confirm that the cipher text successfully decrypts with Bob's private key? My concern is that Eve swaps out the cipher text for a text that only decrypts with her key and Bob can't tell. At a later point then when Bob wants to decrypt he can't and now has no 'power' over when the ciphertext is revealed. What can Bob do? I strayed into homomorphic encryption on my search, that perhaps Bob could process the data in a way that allowed him to tell, but that perhaps is over kill. Then I found that perhaps a zero knowledge proof helps here, but I suspect there is something similar Bob can do to know at the point that Eve hands back the ciphertext Bob can immediately check that it was indeed encrypted by Bob as well and all is ok?

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multiparty-computation

poncho

6/26/24, 7:41 PM

"is there anything Bob can do to confirm that the cipher text successfully decrypts with Bob's private key?"; normally, given $E_{eve}(E_{bob}(M))$, Bob couldn't 'decrypt' it - unless we're talking about "commutative encryption', that is, one for which $E_a(E_b(M)) = E_b(E_a(M))$ always holds. Is that the case you're asking about?

amlwwalker

6/27/24, 9:43 AM

yes exactly @poncho - in this case (())=(()) can Bob check to see that eve hasn't swapped the cipher text out so that its now just () ? And the more complex case where its, for instance case ((c(d()))) - can any of ,c,d check independently whether the cipher text has been swapped out for just () ? In the case of ((c(d()))) if Bob decrypts it, you end up with (c(d())) - which is fine, i just want to know if Bob can verify it decrypted successfully or they had been removed and is no longer one of the keys?

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EN: verifying that a private key can decrypt a payload in multi key encryption

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