# Ciphertexts equality testing in CKKS

**URL:** <https://openfhe.discourse.group/t/ciphertexts-equality-testing-in-ckks/1033>\
**Category:** FHE Questions\
**Created:** [January 23, 2024, 3:43pm UTC](https://openfhe.discourse.group/t/ciphertexts-equality-testing-in-ckks/1033 "2024-01-23T15:43:44Z")\
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**Author:** ![mchenu](https://avatars.discourse-cdn.com/v4/letter/m/ba9def/32.png) [@mchenu](https://openfhe.discourse.group/u/mchenu)\
**Post date:** [January 23, 2024, 3:43pm UTC](https://openfhe.discourse.group/t/ciphertexts-equality-testing-in-ckks/1033/1 "2024-01-23T15:43:44Z")

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Hi,  
As the CKKS scheme is using noise, is there a way to know if two ciphertexts are actually encrypting the same data (without having the private key obviously)? That is, if c1 and c2 are both encrypting an element m, both with the same public key and same scheme parameters, we have c1 != c2 but is there a operation allowing to detect that they are encrypting the same data? Or is there a security proof on that?

I have seen that by switching to TFHE there is a way to compare ciphertexts however the result is also encrypted, so an attacker without the private key would not know the result.

Any idea/pointers?

Thanks a lot in advance.

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