# How can I implement decryption for NTRU homomorphic encryption scheme?

I have come across this paper On-the-fly multiparty computation via on-the-cloud Multikey from Fully Homomorphic Encryption by Lopez-Alt et al., where authors describe a NTRU-based homomorphic encryption scheme suitable for a multikey context. Multikey means each party encrypts its input with its unique key, the server computes homomorphically some evaluations and in the final stage, parties run an MPC protocol for decryption.

I have not understood this phase yet and I can imagine two ways to do it :

What is the correct implementation ?

• Section 4 of that paper describes an MPC protocol $\Pi_{DEC}$ for computing the NTRU decryption procedure – cygnusv Jan 19 '16 at 9:36
• Cygnusv, will you be more explicit about how is that MPC protocol implemented ? From what I have understood, that section describes how decryption protocol should behave. Also in section 4 of On-the-fly multiparty computation via on-the-cloud Multikey from Fully Homomorphic Encryption by Lopez-Alt et al., authors emphasize how parties can prove they are honest and how the server can prove that it had done the computation correctly. But I have the feeling that I am missing something, please point it to me. I would be very grateful. – guglielmo london Jan 20 '16 at 21:33
• I have read those papers again and have taken both solutions into account. So far, I am convinced that the NTRU decryption is computed as a function by a MPC protocol, based on BGV. From my point of view, it is something similar to Homomorphic Evaluation of the AES Circuit. The NTRU decryption is a multiplication between the ciphertext and the parties secret keys, so the parties encrypt their secret keys, encrypt the NTRU ciphertext, the cloud computes the decryption function and gives parties the answer encrypted with BGV. – guglielmo london Jan 20 '16 at 21:42
• A MPC protocol derived from homomorphic NTRU ? I think this would be an interesting thing.But I guess it should be used another approach. For me, the template from Multiparty Computation with Low Communication, Computation and Interaction via Threshold FHE by Asharov et al does not seem an option. – guglielmo london Jan 20 '16 at 21:47