International Association for Cryptologic Research

International Association
for Cryptologic Research


Jaspal Singh


Private Set Operations from Oblivious Switching 📺
Private set intersection reveals the intersection of two private sets, but many real-world applications require the parties to learn $\textit{only}$ partial information} about the intersection. In this paper, we introduce a new approach for computing arbitrary functions of the intersection, provided that it is safe to also reveal the cardinality of the intersection. In the most general case, our new protocol provides the participants with secret shares of the intersection, which can be fed into any generic 2PC protocol. Certain computations on the intersection can also be done even more directly and efficiently, avoiding this secret-sharing step. These cases include computing $\textit{only}$ the cardinality of the intersection, or the ``cardinality-sum'' application proposed in Ion $\textit{et al.}$ (ePrint 2017). Compared to the state-of-the-art protocol for computing on the intersection (Pinkas et al., Eurocrypt 2019), our protocol has about $2.5-3\times$ less communication and has faster running time on slower (50Mbps) networks. Our new techniques can also be used to privately compute the {\em union} of two sets as easily as computing the intersection. Our protocol concretely improves the leading private set union protocol (Kolesnikov et al., Asiacrypt 2020) by a factor of $2-2.5\times$, depending on the network speed. We then show how private set union can be used in a simple way to realize the ``Private-ID'' functionality suggested by Buddhavarapu et al.~(ePrint 2020). Our protocol is significantly faster than the prior Private-ID protocol, especially on fast networks. All of our protocols are in the two-party setting and are secure against semi-honest adversaries.
Large Message Homomorphic Secret Sharing from DCR and Applications 📺
Jaspal Singh Lawrence Roy
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.