Private Multiparty Sampling and Approximation of Vector Combinations

Abstract

a b s t r a c tWe consider the problem of private efficient data mining of vertically-partitioned databases. Each of several parties holds a column of a data matrix (a vector) and the parties want to investigate the componentwise combination of their vectors. The parties want to minimize communication and local computation while guaranteeing privacy in the sense that no party learns more than necessary. Sublinear-communication private protocols have primarily been studied only in the two-party case. In contrast, this work focuses on multiparty settings.First, we give efficient private multiparty protocols for sampling a row of the data matrix and for computing arbitrary functions of a random row, where the row index is additively shared among two or more parties. These results can be used to obtain private approximation protocols for several useful combination functionalities. Moreover, these results have some interesting consequences for the general problem of reducing sublinear-communication secure multiparty computation to two-party private information retrieval (PIR).Second, we give protocols for computing approximations (summaries) of the componentwise sum, minimum, and maximum of the columns. Here, while providing a weaker privacy guarantee (where the approximation may leak up to the entire output vector), our protocols are extremely efficient. In particular, the required cryptographic overhead (compared to non-private solutions) is polylogarithmic in the number of rows.

Near-optimal private approximation protocols via a black box transformation

“…, M } n , and the max-dominance norm is n j=1 max(xj, yj). This problem, and its generalization, the dominant p-norm, defined as ( n j=1 max(xj, yj) p ) 1/p for p > 0, are studied in [19,53,56,57,58] (in [40] this problem is instead studied for p < 0, which is useful for coordinatewise minima). There are no sharply concentrated NBEs known for p > 0.…”

“…Ishai et al [40] introduce the multi-party model for private approximation protocols, and study a relaxed notion of privacy in it. If there are s parties with respective inputs x 1 , .…”

Communication-Efficient Private Protocols for Longest Common Subsequence

“…Alternatively, perhaps neither Alice nor Bob want to play the role of the server (who pre-computes the basic block function table) but instead want to leverage the resources of one or more external servers, without having to trust them. We can generalize our LCS-length and LCS-backtracking protocols to this scenario using a multiparty generalization of indirect indexing [17,24]. In particular, the multiparty indirect indexing scheme of Ishai et al [24] is a general construction using any 2-round OT protocol.…”

“…We can generalize our LCS-length and LCS-backtracking protocols to this scenario using a multiparty generalization of indirect indexing [17,24]. In particular, the multiparty indirect indexing scheme of Ishai et al [24] is a general construction using any 2-round OT protocol. To achieve a construction with polylogarithmic communication complexity, Ishai et al use an OT scheme based on PIR with length-flexible messages (achieved using a length-flexible homomorphic encryption scheme such as Damgård-Jurik [15,16]).…”

Multi-party Indirect Indexing and Applications

“…In concurrent and independent work, Ishai et al [21] design an mOT protocol under the name "distributed OT." Both our protocol and theirs involve the use of efficient PIR protocols, though in different ways.…”