Adding Distributed Decryption and Key Generation to a Ring-LWE Based CCA Encryption Scheme.

We show how to build distributed key generation and distributed decryption procedures for the \(\textsf {LIMA} \) Ring-LWE based post-quantum cryptosystem. Our protocols implement the CCA variants of distributed decryption and are actively secure (with abort) in the case of three parties and honest majority. Our protocols make use of a combination of problem specific MPC protocols, generic garbled circuit based MPC and generic Linear Secret Sharing based MPC. We also, as a by-product, report on the first run-times for the execution of the SHA-3 function in an MPC system.