Is there such a cryptography where I can prove that someone decrypted an encrypted string? Say I wanted to attach a Bitcoin private key in some type of digital container, but in order to open this digital container, I would need to break a digital seal.

I'm basically trying to find a digital equivalent of how a security wax seal works to make a letter tamperproof:

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What is the digital equivalent of this? I can write down a bitcoin private key in the envelope and have a wax seal on it. But how do I do this via email?

  • $\begingroup$ If I break AES or DSA I'll not tell anybody! $\endgroup$ – kelalaka Sep 23 '20 at 19:59
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    $\begingroup$ One fundamental obstacle to this is that for (classical) computation, digital information is cloneable. In particular, if you give me such a digital object $D$, I can copy this to get $D'$. Then, even if I break the "wax seal" on $D'$, this is now not connected to $D$. This isn't to say that it is impossible, but that any method must deal with the above obstacle. For example, in the quantum setting the "cloning" arguments break down, but this may be less interesting for your purpose. $\endgroup$ – Mark Sep 23 '20 at 19:59
  • $\begingroup$ Looks like this would require a centralized server in order to detect if a digital lock was opened or not. $\endgroup$ – Patoshi パトシ Sep 23 '20 at 21:27
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    $\begingroup$ I agree with the above comments, this seems to require either a trusted central authority, or the use of quantum computation. $\endgroup$ – Geoffroy Couteau Sep 23 '20 at 22:19
  • $\begingroup$ Note that knowing if someone accessed the secret is quite different than making them unable to modify it! (and as a sidenote, wax seals weren't perfect, either) $\endgroup$ – Ángel Sep 24 '20 at 0:59

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