What is the threshold multi-party secret sharing case? Which article is referenced in the implementation

I suggest reading https://www.pnas.org/doi/10.1073/pnas.2304415120 to learn about use cases and underlying crypto (alternatively, you can go the eprint version: Collaborative Privacy-Preserving Analysis of Oncological Data using Multiparty Homomorphic Encryption). Other notable papers on threshold FHE + use cases are

- Multiparty Homomorphic Encryption from Ring-Learning-With-Errors
- [2009.00349] POSEIDON: Privacy-Preserving Federated Neural Network Learning
- Truly privacy-preserving federated analytics for precision medicine with multiparty homomorphic encryption | Nature Communications

OpenFHE implements most of the threshold FHE features described in these papers.

I remember the threshold ckks in the previous version was based on Multiparty computation with low communication, computation, and interaction via threshold fhe. However, this version now has the feature of secret sharing. If I want to cite articles in my paper, which ones should I cite

For the OpenFHE implementation, I would cite the following papers:

- Multiparty Computation with Low Communication, Computation and Interaction via Threshold FHE | SpringerLink
- Multiparty Homomorphic Encryption from Ring-Learning-With-Errors
- https://www.pnas.org/doi/10.1073/pnas.2304415120

Note that secret sharing is an inherent feature of threshold FHE proposed in the first paper. The other two papers proposed further improvements, like interactive bootstrapping.

ok,This article of Multiparty computation with low communication, computation, and interaction via threshold fhe is about the homomorphism of the threshold, but it doesn’t seem to say how to recover the private key for decryption when one party is offline. Is the threshold ckks implemented in the previous version of OpenFHE reference to this article that can recover the disconnection, or is it just called threshold ckks but without corresponding functionality? Another question is whether the implemented threshold ckks are all based on secret sharing

Another question I would like to ask is, when writing about the threshold ckk algorithm, can I refer to the algorithm in Collaborative Privacy Resilience Analysis of Online Data Using Multiparty Homomorphic Encryption? Can I use it without making any changes, because I also don’t know how to express the same algorithm in different words

First, I suggest reading this topic: I would like to ask if there are any differences between the latest version of the threshold scheme and the previous one - #2 by ypolyakov

Second, I suggest reading the README for threshold FHE encryption (https://github.com/openfheorg/openfhe-development/blob/dev/docs/static_docs/Threshold_FHE.md). The last section deals with the t-out-of-N case (Threshold decryption with Aborts).

Are you referring to the PNAS paper cited above (it has a different but somewhat similar title) or some other paper?