TY - JOUR
T1 - Private multiparty sampling and approximation of vector combinations
AU - Ishai, Yuval
AU - Malkin, Tal
AU - Strauss, Martin J.
AU - Wright, Rebecca N.
N1 - Funding Information:
The first author was supported in part by ISF grant 1310/06 and BSF grant 2004361; the work was partially completed while he was visiting UCLA. The second author was supported in part by NSF grant CCF-0347839 and NSF grant CNS-0716245. The third author was supported in part by NSF grant DMS-0510203 and NSF grant DMS-0354600. The fourth author was supported in part by NSF grant CNS-0822269.
PY - 2009/4/17
Y1 - 2009/4/17
N2 - We 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 multi-party 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.
AB - We 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 multi-party 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.
KW - Approximation algorithms
KW - Secure multiparty computation
KW - Sublinear-communication algorithms
UR - http://www.scopus.com/inward/record.url?scp=62149090255&partnerID=8YFLogxK
U2 - 10.1016/j.tcs.2008.12.062
DO - 10.1016/j.tcs.2008.12.062
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AN - SCOPUS:62149090255
SN - 0304-3975
VL - 410
SP - 1730
EP - 1745
JO - Theoretical Computer Science
JF - Theoretical Computer Science
IS - 18
ER -