TY - GEN

T1 - On Private Computation in Incomplete Networks

AU - Beimel, Amos

N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2005

Y1 - 2005

N2 - Suppose that some parties are connected by an incomplete network of reliable and private channels. The parties cooperate to execute some protocol. However, the parties are curious - after the protocol terminates each processor tries to learn information from the communication it heard. We say that a function can be computed privately in a network if there is a protocol in which each processor learns only the information implied by its input and the output of the protocol. The question we address in this paper is what functions can be computed privately in a given incomplete network. It is known that if a network is 2-connected then every pair of parties can communicate privately. Thus, the question is interesting only for non-2-connected networks. We first characterize the functions that can be computed privately in simple networks - networks with one separating vertex and two 2-connected components. We then deal with private computations in arbitrary networks: we reduce this question to private computations of related functions on trees, and give sufficient and necessary conditions on the functions that can be computed privately on trees.

AB - Suppose that some parties are connected by an incomplete network of reliable and private channels. The parties cooperate to execute some protocol. However, the parties are curious - after the protocol terminates each processor tries to learn information from the communication it heard. We say that a function can be computed privately in a network if there is a protocol in which each processor learns only the information implied by its input and the output of the protocol. The question we address in this paper is what functions can be computed privately in a given incomplete network. It is known that if a network is 2-connected then every pair of parties can communicate privately. Thus, the question is interesting only for non-2-connected networks. We first characterize the functions that can be computed privately in simple networks - networks with one separating vertex and two 2-connected components. We then deal with private computations in arbitrary networks: we reduce this question to private computations of related functions on trees, and give sufficient and necessary conditions on the functions that can be computed privately on trees.

UR - http://www.scopus.com/inward/record.url?scp=24944450284&partnerID=8YFLogxK

U2 - 10.1007/11429647_4

DO - 10.1007/11429647_4

M3 - Conference contribution

AN - SCOPUS:24944450284

SN - 9783540260523

T3 - Lecture Notes in Computer Science

SP - 18

EP - 33

BT - Structural Information and Communication Complexity

A2 - Pelc, Andrzej

A2 - Raynal, Michel

PB - Springer

T2 - 12 International Colloquium on Structural Information and Communication Complexity, SIROCCO 2005

Y2 - 24 May 2005 through 26 May 2005

ER -