| Title | : | Distributed Secrets in Cryptography: Multikey Homomorphic Encryption and Secret Sharing |
| Speaker | : | Raghavendra Vernekar (MS Scholar - IITM) |
| Details | : | Tue, 8 Aug, 2023 4:00 PM @ MR - I (SSB 233) |
| Abstract: | : | We study distributed secrets in cryptography, when these are generated independently as well as when they are generated in a correlated manner. In the former setting, we study the notion of multikey homomorphic encryption where users can generate their own public and secret keys independently but nevertheless have an untrusted third party evaluator compute on ciphertexts generated using these independent public keys. In the latter setting, we study the classical notion of secret sharing and build upon the recently introduced notion of “adept secret sharingâ€. Our contributions are summarized as: 1. We provide the first multi-key homomorphic encryption scheme from pairings. Our scheme supports multiple users who can generate their keys independently, and permits an unbounded number of additions and a single multiplication on the ciphertexts generated by the users. Our scheme relies on the standard SXDH assumption on pairings. Previously, such a scheme was only known in the single user setting [BGN05], which we generalize to the multi-user setting. 2. We study the notion of adept secret sharing of [BDR20] and show that for a certain special case, their “error reconstruction†algorithm, which is exponential time in general, can be made polynomial time. In more detail, we use an idea proposed by [MPS11] in the context of a slightly weaker notion called “error decodability†in the context of error correction. By combining error decodable secret sharing with (a weaker form of) adept secret sharing, we design an efficient error correction for the same special case of access structures studied by [MPS11]. |
