I want to implement threshold homomorphic encryption for my project. (encrypt a message using one public key, and decrypt a ciphertext using distributed secret keys)

I read a paper "Multiparty computation from threshold homomorphic encryption", which describes the way to build threshold homomorphic encryption.

However, in a case of Paillier cryptosystem, the performance was not good than I expected. (http://cs.utdallas.edu/dspl/cgi-bin/pailliertoolbox/manual.pdf)

I recently read that NTRU based cryptosystem provides homomorphism and the performance is better than others.

So I think that NTRU-based threshold homomorphic system will have better performance.

But I could not find the paper about NTRU-based threshold homomorphic encryption system.

I think it is possible to build the NTRU-based one because there are some references about NTRU-based secret sharing schemes.

Is there any paper that explains NTRU-based threshold homomorphic encryption system?

Or can anyone give me a guide to build the system?

  • $\begingroup$ Is there a specific reason you need use a threshold homomorphic system, or will any threshold public key decryption system meet your needs? The latter problem is a lot easier/more efficient... $\endgroup$ – poncho Oct 27 '17 at 13:38
  • $\begingroup$ @poncho I need additive homomorphism, because I want to build distributed cloud system using threshold homomorphic system. $\endgroup$ – takita Oct 29 '17 at 9:40
  • $\begingroup$ Have a look at this paper On-the-fly Multiparty Computation on the cloud via Multikey HE and there other papers that discuss threshold homomorphic encryption schemes on eprint.iacr archive. $\endgroup$ – guglielmo london Nov 11 '17 at 16:49
  • $\begingroup$ @guglielmolondon Actually, I already read it. But In the case of the paper, the public key is not the only one. So it is not what I wanted. $\endgroup$ – takita Nov 12 '17 at 7:04

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