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Is there a cryptographic (or even not entirely cryptographic) way of exchanging objects between Alice and Bob that would not require a third party, and Alice and Bob would not need to trust each other? For example, Alice and Bob have Y and X objects (some information) and want to exchange them (in other words both Alice and Bob after transaction will have access to the set Y∪X). How can they do this directly to each other?

Is it possible to solve this problem, for example, using private keys, zk-proofs, etc? Is it possible to solve it in principle?

Thank you!

Lee
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    The fundamental problem is - how does Alice know that Bob is Bob? Perhaps you say "because he has Bob's private key", but that just shifts the problem - then how does Alice know that that private key actually belongs to Bob? – user253751 Mar 18 '18 at 01:49

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No, without some kind of trusted information there is no way of identifying the parties, so Alice and Bob are never able to trust that they have transferred the data to the right party.

Even if they meet in person they need to have some trusted data (such as facial features of a person, remembered from when they met before) otherwise they may confer data to an imposter.

I'm assuming here that you need to keep the data confidential. That is not apparent from your question. If this isn't the case Alice and Bob could simply publish the information for all to see.

Of course, Alice and Bob would still not be confident that the right entity posted the data, i.e. the authenticity of the data cannot be proved.

Maarten Bodewes
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Yes, there are cryptoeconomic schemes. See here.

Randomblue
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