STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Completeness theorems for non-cryptographic fault-tolerant distributed computation
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Multiparty unconditionally secure protocols
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Non-cryptographic fault-tolerant computing in constant number of rounds of interaction
Proceedings of the eighth annual ACM Symposium on Principles of distributed computing
A zero-one law for Boolean privacy
SIAM Journal on Discrete Mathematics
Communication complexity of secure computation (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Privacy and communication complexity
SIAM Journal on Discrete Mathematics
A minimal model for secure computation (extended abstract)
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Private Computations Over the Integers
SIAM Journal on Computing
Amortizing randomness in private multiparty computations
PODC '98 Proceedings of the seventeenth annual ACM symposium on Principles of distributed computing
A Randomness-Rounds Tradeoff in Private Computation
SIAM Journal on Discrete Mathematics
Characterizing linear size circuits in terms of privacy
Journal of Computer and System Sciences
Extracting randomness: a survey and new constructions
Journal of Computer and System Sciences
Randomness complexity of private computation
Computational Complexity
Modern Cryptography, Probabilistic Proofs, and Pseudorandomness
Modern Cryptography, Probabilistic Proofs, and Pseudorandomness
A Theorem on Sensitivity and Applications in Private Computation
SIAM Journal on Computing
Randomness in Private Computations
SIAM Journal on Discrete Mathematics
On the Number of Random Bits in Totally Private Computation
ICALP '95 Proceedings of the 22nd International Colloquium on Automata, Languages and Programming
On the randomness complexity of efficient sampling
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Secure computations in a minimal model using multiple-valued ESOP expressions
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
Hi-index | 0.00 |
We consider the amount of randomness necessary in information-theoretic private protocols. We prove that at least Ω(log n) random bits are necessary for the t-private computation of the function xor by n players, for any t ≥ 2. In view of the upper bound of O(t2log(n/t))[19], this bound is tight, up to constant factors, for any fixed t. For a class of protocols obeying certain restrictions, we give stronger lower bounds of Ω(t log (n/t)). We note that all known randomness efficient private protocols designed specifically for xor belong to this class. All our lower bounds hold for the "trusted dealer" model as well, and the Ω(t log (n/t)) lower bound for restricted protocols is tight, up to constant factors, for any t ≥ 2 in this model.In comparison, the previous lower bounds on the amount of randomness required by t-private computation of explicit functions did not grow with n for constant values of t, and our results improve the previous lower bounds for xor for any 2 ≤ t = o(log n). Our results also show that already for t = 2, Ω(log n) random bits are necessary, while it is known that for the case of t = 1 a single random bit is sufficient for privately computing xor for any number of players.Our proofs use novel techniques by which we extract random variables from a t-private protocol, and then use the t-privacy property of the protocol to prove properties of these random variables. These properties in turn imply that the number of random bits used by the players is large.