# Can you prove a decryption without revealing the key?

**URL:** https://boards.straightdope.com/t/can-you-prove-a-decryption-without-revealing-the-key/965090
**Category:** Factual Questions
**Created:** [May 25, 2022, 5:40pm UTC](https://boards.straightdope.com/t/can-you-prove-a-decryption-without-revealing-the-key/965090 "2022-05-25T17:40:49Z")
**Posts on this page:** 2
**Page:** 3

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### Author: ![scabpicker](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/scabpicker/32/8268_2.png) [@scabpicker](https://boards.straightdope.com/u/scabpicker)
#### Post date: [June 1, 2022, 7:11pm UTC](https://boards.straightdope.com/t/can-you-prove-a-decryption-without-revealing-the-key/965090/41 "2022-06-01T19:11:28Z")

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Yeah, that was my initial thought. Some people up thread say it doesn’t prove Mallory isn’t surveilling the Eves in that case. If she did have that capability, Mallory probably owns them.

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### Author: ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)
#### Post date: [June 1, 2022, 9:13pm UTC](https://boards.straightdope.com/t/can-you-prove-a-decryption-without-revealing-the-key/965090/42 "2022-06-01T21:13:31Z")

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There’s another method, I think. There is a technique called [homomorphic encryption](https://en.wikipedia.org/wiki/Homomorphic_encryption) that allows performing computations on encrypted data. I’m not sure if the current level of development allows this, but in principle Mallory could distribute a decryptor that only operates on data that has been encrypted using her public key. The Eves could use this to verify that Mallory had the key without Mallory revealing said key.

Say Eve generates a message M. She encrypts it with Bob’s public key to Eb(M), and then again with Mallory’s public key to Em(Eb(M)).

The homomorphic decryptor can then perform the transformation Hmb(Em(Eb(M))) =\> Em(M), by decrypting the message inside the “container” locked with Mallory’s key. Eve can verify this result by encrypting the plain message with Mallory’s public key and comparing against the result from the homomorphic system.

Eve can do all of this offline, as many times as required, so even if she was compromised once, she can hopefully avoid that problem next time.

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