Private Computations over the Integers

The subject of this work is the possibility of private distributed computations of $n$-argument functions defined over the integers. A function $f$ is $t$-private if there exists a protocol for computing $f$, so that no coalition of at most $t$ participants can infer any additional information from...

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Veröffentlicht in:SIAM journal on computing Jg. 24; H. 2; S. 376 - 386
Hauptverfasser: Chor, Benny, Geréb-Graus, Mihály, Kushilevitz, Eyal
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Philadelphia, PA Society for Industrial and Applied Mathematics 01.04.1995
Schlagworte:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Boolean
Communication
Computer science
Computer science; control theory; systems
Exact sciences and technology
Logical, boolean and switching functions
Privacy
Protocol
Theoretical computing
Integer
Addition
Boolean function
Computing
Distributed computing
Communication
Complexity
ISSN:0097-5397, 1095-7111
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Zusammenfassung:The subject of this work is the possibility of private distributed computations of $n$-argument functions defined over the integers. A function $f$ is $t$-private if there exists a protocol for computing $f$, so that no coalition of at most $t$ participants can infer any additional information from the execution of the protocol. It is known that over finite domains every function can be computed $\lfloor (n - 1)/2 \rfloor $-privately. Some functions, like addition, are even $n$-private. We prove that this result cannot be extended to infinite domains. The possibility of privately computing $f$ is shown to be closely related to the communication complexity of $f$. By using this relation, we show, for example, that $n$-argument addition is $\lfloor (n - 1)/2 \rfloor $-private over the nonnegative integers, but not even 1-private over all the integers. Finally, a complete characterization of $t$-private Boolean functions over countable domains is given. A Boolean function is 1-private if and only if its communication complexity is bounded. This characterization enables us to prove that every Boolean function falls into one of the following three categories: It is either $n$-private, $\lfloor (n - 1)/2 \rfloor $-private but not $\lceil n/2 \rceil$-private, or not 1-private.
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ISSN:0097-5397
1095-7111
DOI:10.1137/S0097539791194999