Yuval Ishai

Elette Boyle, Itai Dinur, Niv Gilboa et al.

Can we sense our location in an unfamiliar environment by taking a sublinear-size sample of our surroundings? Can we efficiently encrypt a message that only someone physically close to us can decrypt? To solve this kind of problems, we introduce and study a new type of hash functions for finding shifts in sublinear time. A function $h:\{0,1\}^n\to \mathbb{Z}_n$ is a $(d,δ)$ {\em locality-preserving hash function for shifts} (LPHS) if: (1) $h$ can be computed by (adaptively) querying $d$ bits of its input, and (2) $\Pr [ h(x) \neq h(x \ll 1) + 1 ] \leq δ$, where $x$ is random and $\ll 1$ denotes a cyclic shift by one bit to the left. We make the following contributions. * Near-optimal LPHS via Distributed Discrete Log: We establish a general two-way connection between LPHS and algorithms for distributed discrete logarithm in the generic group model. Using such an algorithm of Dinur et al. (Crypto 2018), we get LPHS with near-optimal error of $δ=\tilde O(1/d^2)$. This gives an unusual example for the usefulness of group-based cryptography in a post-quantum world. We extend the positive result to non-cyclic and worst-case variants of LPHS. * Multidimensional LPHS: We obtain positive and negative results for a multidimensional extension of LPHS, making progress towards an optimal 2-dimensional LPHS. * Applications: We demonstrate the usefulness of LPHS by presenting cryptographic and algorithmic applications. In particular, we apply multidimensional LPHS to obtain an efficient "packed" implementation of homomorphic secret sharing and a sublinear-time implementation of location-sensitive encryption whose decryption requires a significantly overlapping view.

Ingerid Fosli, Yuval Ishai, Victor I. Kolobov et al.

A homomorphic secret sharing (HSS) scheme is a secret sharing scheme that supports evaluating functions on shared secrets by means of a local mapping from input shares to output shares. We initiate the study of the download rate of HSS, namely, the achievable ratio between the length of the output shares and the output length when amortized over $\ell$ function evaluations. We obtain the following results. * In the case of linear information-theoretic HSS schemes for degree-$d$ multivariate polynomials, we characterize the optimal download rate in terms of the optimal minimal distance of a linear code with related parameters. We further show that for sufficiently large $\ell$ (polynomial in all problem parameters), the optimal rate can be realized using Shamir's scheme, even with secrets over $\mathbb{F}_2$. * We present a general rate-amplification technique for HSS that improves the download rate at the cost of requiring more shares. As a corollary, we get high-rate variants of computationally secure HSS schemes and efficient private information retrieval protocols from the literature. * We show that, in some cases, one can beat the best download rate of linear HSS by allowing nonlinear output reconstruction and $2^{-Ω(\ell)}$ error probability.

Dan Boneh, Elette Boyle, Henry Corrigan-Gibbs et al.

This paper presents Poplar, a new system for solving the private heavy-hitters problem. In this problem, there are many clients and a small set of data-collection servers. Each client holds a private bitstring. The servers want to recover the set of all popular strings, without learning anything else about any client's string. A web-browser vendor, for instance, can use Poplar to figure out which homepages are popular, without learning any user's homepage. We also consider the simpler private subset-histogram problem, in which the servers want to count how many clients hold strings in a particular set without revealing this set to the clients. Poplar uses two data-collection servers and, in a protocol run, each client send sends only a single message to the servers. Poplar protects client privacy against arbitrary misbehavior by one of the servers and our approach requires no public-key cryptography (except for secure channels), nor general-purpose multiparty computation. Instead, we rely on incremental distributed point functions, a new cryptographic tool that allows a client to succinctly secret-share the labels on the nodes of an exponentially large binary tree, provided that the tree has a single non-zero path. Along the way, we develop new general tools for providing malicious security in applications of distributed point functions.

Samuel Dittmer, Yuval Ishai, Steve Lu et al.

In this work we describe a token-based solution to Contact Tracing via Distributed Point Functions (DPF) and, more generally, Function Secret Sharing (FSS). The key idea behind the solution is that FSS natively supports secure keyword search on raw sets of keywords without a need for processing the keyword sets via a data structure for set membership. Furthermore, the FSS functionality enables adding up numerical payloads associated with multiple matches without additional interaction. These features make FSS an attractive tool for lightweight privacy-preserving searching on a database of tokens belonging to infected individuals.

Siddharth Garg, Zahra Ghodsi, Carmit Hazay et al.

In several settings of practical interest, two parties seek to collaboratively perform inference on their private data using a public machine learning model. For instance, several hospitals might wish to share patient medical records for enhanced diagnostics and disease prediction, but may not be able to share data in the clear because of privacy concerns. In this work, we propose an actively secure protocol for outsourcing secure and private machine learning computations. Recent works on the problem have mainly focused on passively secure protocols, whose security holds against passive (`semi-honest') parties but may completely break down in the presence of active (`malicious') parties who can deviate from the protocol. Secure neural networks based classification algorithms can be seen as an instantiation of an arithmetic computation over integers. We showcase the efficiency of our protocol by applying it to real-world instances of arithmetized neural network computations, including a network trained to perform collaborative disease prediction.