Homomorphic Encryption: Eval Ciphertexts with different Public Keys

Maxim

11/24/23, 5:44 PM

I am trying to get into HE and Federated Learning and found the following Paper: https://arxiv.org/pdf/2204.07752.pdf

The Main Concepts are clear to me, but I do not understand how or if you can Evaluate multiple Ciphertext that are encrypted with different Public keys. If it is possible- how? And how does the decryption work?

Other Question: is it generally possible to add or multiply two ciphertexts from different origins and let them be decrypted from each instance individually (without communication or some sort of key exchange between two participants) ?

I am thinking the following Setup: Two Users send their data or model weights to a central server that calculates the general model weights and sends them back to both clients. Both clients should be able to decrypt the result. Just like in the Paper. But how does it work?

Maybe somebody could recommend a paper or explain it. Thanks in regard :)

0 + 1

multiparty-computation

homomorphic-encryption

fgrieu

11/24/23, 8:48 PM

Please [edit](https://crypto.stackexchange.com/posts/102950/edit) the question to clarify what's wanted! As it stands now: given a public key and any plaintext (that we can choose), we can evaluate a ciphertext. We can repeat this process, including with different public keys. I can't see why that would not match _"Evaluate multiple Ciphertext that are encrypted with different Public keys"_. Decryption is possible with the private keys. And we can _"multiply two ciphertexts"_ or pretty much any things that we can turn to integers (e.g. by big-endian convention).

Elon Musk

I sit in a Tesla and translated this thread with Ai:

EN: Homomorphic Encryption: Eval Ciphertexts with different Public Keys

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