[Resource Topic] 2021/274: Large Message Homomorphic Secret Sharing from DCR and Applications

Welcome to the resource topic for 2021/274

Title:
Large Message Homomorphic Secret Sharing from DCR and Applications

Authors: Lawrence Roy, Jaspal Singh

Abstract:

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 multi-server ORAM with constant bandwidth overhead, and a rate-1 trapdoor hash function with negligible error rate.

ePrint: https://eprint.iacr.org/2021/274

Talk: https://www.youtube.com/watch?v=3Ak8rXRkvmc

See all topics related to this paper.

Feel free to post resources that are related to this paper below.

Example resources include: implementations, explanation materials, talks, slides, links to previous discussions on other websites.

For more information, see the rules for Resource Topics .