Characterizing linear size circuits in terms of privacy
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Randomness in private computations
PODC '96 Proceedings of the fifteenth annual ACM symposium on Principles of distributed computing
Amortizing randomness in private multiparty computations
PODC '98 Proceedings of the seventeenth annual ACM symposium on Principles of distributed computing
A theorem on sensitivity and applications in private computation
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Private Computations in Networks: Topology versus Randomness
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Private Computation - k-Connected versus 1-Connected Networks
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Lower bounds on the amount of randomness in private computation
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Linear integer secret sharing and distributed exponentiation
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
Proactive verifiable linear integer secret sharing scheme
ICICS'09 Proceedings of the 11th international conference on Information and Communications Security
| Hi-index | 0.00 |
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 $\left\lfloor{(n-1)/2}\right\rfloor$-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 $f$. Using this relation, we show, for example, that $n$-argument addition is $\left\lfloor{(n-1)/2}\right\rfloor$-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, $\left\lfloor{(n-1)/2}\right\rfloor$-private but not $\left\lceil{n/2}\right\rceil $-private, or not $1$-private.