Hello everyone 
I have 2 questions regarding THFE.
I am looking for a description of THFE for CKKS that precisely explains how the encryption protocol, decryption protocol, and interactive bootstrapping work.
Question 1:
I found the following resource from OpenFHE:
Question 2:
If I move the homomorphic computation to the cloud, including bootstrapping, how would the interactive bootstrapping inTHFE work? How is it triggered? This is not entirely clear to me. Thank you for your help.
Yes, these resources are still valid. I suggest reading Appendices D and E of Collaborative Privacy-Preserving Analysis of Oncological Data using Multiparty Homomorphic Encryption to learn more about interactive bootstrapping. The algorithm described in Appendix E is already part of OpenFHE.
Thats Great it helps a lot.
Hi @ypolyakov, I’ve read both Appendices D and E. My understanding is that during interactive bootstrapping, the server conducts computations. Once the ciphertext is depleted, it sends it back to the client, which then rejuvenates it by applying a rounding function.
However, what I haven’t grasped yet is this: If multiple parties are computing, say 6 of them, and there’s only one computation server, will the same bootstrapping process be followed? Will the depleted ciphertext then be returned to the parties, where each will partially decrypt it and perform a rounding function? Subsequently, will the results be aggregated across all 6 parties, and the refreshed ciphertext sent back to the server to continue the computations?
I’m having trouble discerning the essential difference between the two-party and multi-party protocols. thanks in advance
In the threshold FHE setting, a number n of parties jointly create the keys and jointly decrypt. In principle, all other evaluation operations can be done non-interactively at each party. However, for efficiency reasons, given the overhead of single-party bootstrapping, a faster interactive bootstrapping procedure between the n parties was introduced and is made available in OpenFHE. This scenario is where all n parties do the same computations and is the one in Appendix E.
Now let’s consider the scenario where you have a separate computing server that you want to perform all evaluations, and the n parties only create the keys and decrypt. In this case, the computing server will act as the server in a typical client-server FHE computation–but where there are n clients–and would perform the single-party bootstrapping procedure (with the caveat that the parameters of the single-party bootstrapping need to be set larger due to the threshold setting).
Finally, when you have a two-party scenario, but you want one of the parties to do the bulk of the computation, there is a more efficient particularization of the n-party interactive bootstrapping, which is the two-party interactive bootstrapping procedure described in Appedix D. This is not yet available in OpenFHE.
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Thank u very much @andreea.alexandru . That Helps me