Large Message Homomorphic Secret Sharing from DCR and Applications
We present the first homomorphic secret sharing (HSS) construction that simultaneously (1) has negligible correctness error, (2) supports integers from an exponentially large range, and (3) relies on an assumption not known to imply FHE specifically, the Decisional Composite Residuosity (DCR) assumption. This resolves an open question posed by Boyle, Gilboa, and Ishai (Crypto 2016) Homomorphic secret sharing is analogous to fully homomorphic encryption, except the ciphertexts are shared across two non colluding evaluators. Previous constructions of HSS either had non negligible correctness error and polynomial size plaintext space or were based on the stronger LWE assumption. We also present two applications of our technique: a two server ORAM with constant bandwidth overhead, and a rate 1 trapdoor hash function with negligible error rate.
IACR Cryptol. ePrint Arch.