International Association
for Cryptologic Research

Random sampling from specified distributions is an important tool with wide applications for analysis of large-scale data. In this paper we study how to randomly sample when the distribution is partitioned among two parties' private inputs. Of course, a trivial solution is to have one party send a (possibly encrypted) description of its weights to the other party who can then sample over the entire distribution (possibly using homomorphic encryption). However, this approach requires communication that is linear in the input size which is prohibitively expensive in many settings. In this paper, we investigate secure 2-party sampling with sublinear communication for many standard distributions. We develop protocols for L_1, and L_2 sampling. Additionally, we investigate the feasibility of sublinear product sampling, showing impossibility for the general problem and showing a protocol for a restricted case of the problem. We additionally show how such product sampling can be used to instantiate a sublinear communication 2-party exponential mechanism for differentially-private data release.

Secure multi-party computation (MPC) allows multiple parties to perform secure joint computations on their private inputs. Today, applications for MPC are growing with thousands of parties wishing to build federated machine learning models or trusted setups for blockchains. To address such scenarios we propose a suite of novel MPC protocols that maximize throughput when run with large numbers of parties. In particular, our protocols have both communication and computation complexity that decrease with the number of parties. Our protocols build on prior protocols based on packed secret-sharing, introducing new techniques to build more efficient computation for general circuits. Specifically, we introduce a new approach for handling \emph{linear attacks} that arise in protocols using packed secret-sharing and we propose a method for unpacking shared multiplication triples without increasing the asymptotic costs. Compared with prior work, we avoid the $\log |C|$ overhead required when generically compiling circuits of size $|C|$ for use in a SIMD computation, and we improve over folklore ``committee-based'' solutions by a factor of $O(s)$, the statistical security parameter. In practice, our protocol is up to $10X$ faster than any known construction, under a reasonable set of parameters.

We continue the line of work initiated by Katz (Eurocrypt 2007) on using tamper-proof hardware tokens for universally composable secure computation. As our main result, we show an oblivious-transfer (OT) protocol in which two parties each create and transfer a single, stateless token and can then run an unbounded number of OTs. We also show a more efficient protocol, based only on standard symmetric-key primitives (block ciphers and collision-resistant hash functions), that can be used if a bounded number of OTs suffice. Motivated by this result, we investigate the number of stateless tokens needed for universally composable OT. We prove that our protocol is optimal in this regard for constructions making black-box use of the tokens (in a sense we define). We also show that nonblack-box techniques can be used to obtain a construction using only a single stateless token.