(... to be written)
Homomorphic Secret Sharing was introduced during CRYPTO 2016 by Elette Boyle, Niv Gilboa, and Yuval Ishai [BGI16]. A lot of optimizations to HSS was shown in follow-up work [BGI17, BCGIO17]. A nice introduction to HSS can be found in [BGILT17].
An implementation of HSS can be found in [OrruHSS].
Geoffrey Couteau's talk "Homomorphic Secret Sharing, Optimizations and Applications" at ACM CSS 2017, also covering [BCGIO17]:
- [BGI16] Elette Boyle, Niv Gilboa, Yuval Ishai: Breaking the Circuit Size Barrier for Secure Computation under DDH. (extended full pdf via iacr.org 2016/585)
- [BGI17] Elette Boyle, Niv Gilboa, Yuval Ishai: Group-Based Secure Computation, Optimizing Rounds, Communication, and Computation. (full pdf via iacr.org 2017/150)
- [BCGIO17] Elette Boyle, Geoffroy Couteau, Niv Gilboa, Yuval Ishai, Michele Orrù: Homomorphic Secret Sharing, Optimizations and Applications. CCS'17, October 30 - November 3 2017, Dallas TX, USA. (full pdf, preliminary pdf)
- [BGILT17] Elette Boyle, Niv Gilboa, Yuval Ishai, Huijia Lin, Stefano Tessaro: Foundations of Homomorphic Secret Sharing. ITCS 2018. (conference paper, full extended pdf via iacr.org 2017/1248)
- [OrruHSS] Michele Orrù: Homomorphic Secret Sharing (implementation page).