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I've been reading about Zero Knowledge Proofs with some interest, but I'm still unclear if it can be used to solve my real-life problem.

I'm wondering if someone can help me understand a little better how they work - intuitively it seems possible.

Let's assume I have 3 bank accounts with different balances, 1 balance is known, as read-only credentials to access the account are made public, but the second and third accounts are private, with the credentials kept secret.

Would it be possible to use a Zero Knowledge Proof to conclusively prove that the balances of the second and third accounts are what I say they are?

Including a brief description of what a ZKP is:

In cryptography, a zero-knowledge proof or zero-knowledge protocol is a method by which one party (the prover) can prove to another party (the verifier) that a given statement is true, without conveying any information apart from the fact that the statement is indeed true.

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    $\begingroup$ Welcome to math overflow! I think this question might be better received if you included a one-sentence definition of a "zero knowledge proof." I was getting ready to vote to close, because questions about bank balances are basically never on topic, but then googled "zero knowledge proof" and realized what this was about. BTW, I don't know the answer. $\endgroup$
    – David White
    Commented Aug 8, 2017 at 8:15
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    $\begingroup$ I have voted to reopen this question. Zero-knowledge proofs are cryptographic protocols that do require research level mathematics. I find this question to be interesting for mathematical reasons and I would be glad to see what applications mathematics has to bank balances. Finally, MO should encourage new users to ask questions if those questions require research level mathematics. $\endgroup$
    – Joseph Van Name
    Commented Aug 8, 2017 at 11:59
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    $\begingroup$ This question has been cross posted at crypto.stackexchange.com/questions/50714/… $\endgroup$
    – Joseph Van Name
    Commented Aug 8, 2017 at 12:04
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    $\begingroup$ Lewis. Have you heard of Zcash? Zcash is a cryptocurrency that uses zero-knowledge proofs to conceal the data of transactions. The Zcash website says "Zcash payments are published on a public blockchain, but the sender, recipient, and amount of a transaction remain private." $\endgroup$
    – Joseph Van Name
    Commented Aug 8, 2017 at 12:18
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    $\begingroup$ I'm voting to close this question as off-topic because it is cross-posted. $\endgroup$
    – Steven Landsburg
    Commented Sep 26, 2017 at 15:32

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Just to be clear on the definitions.

An interractive ZK proof doesn't communicate any information assuming the verifier is honest. It's why, generally we consider the adversary as an external observer.

"Would it be possible to use a Zero Knowledge Proof to conclusively prove that the balances of the second and third accounts are what I say they are?"

What do you mean exactly by "what I say they are"?

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  • $\begingroup$ I'd expect a zero-knowledge proof to avoid leaking information, even to a dishonest verifier, as long as the prover is honest. $\endgroup$
    – Andreas Blass
    Commented Sep 26, 2017 at 17:47
  • $\begingroup$ If the proof is non interactive, then yeah, you can suppose everything about the verifier. But if the proof is interactive, then sometime (like in the Schnorr protocol) you can't prove the zero-knowledgess, if you don't assume the honesty of the verifier. $\endgroup$
    – Ievgeni
    Commented Sep 27, 2017 at 11:08

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