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
The round complexity of secure protocols
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
A zero-one law for Boolean privacy
SIAM Journal on Discrete Mathematics
A communication-privacy tradeoff for modular addition
Information Processing Letters
Characterizing linear size circuits in terms of privacy
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of 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
Security with Low Communication Overhead
CRYPTO '90 Proceedings of the 10th Annual International Cryptology Conference on Advances in Cryptology
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In this paper we study the randomness complexity needed to distributively perform k XOR computation in a t-private way using constant-round protocols. We show that cover-free families allow the recycling of random bits for constant-round private protocols. More precisely, we show that after an 1-round initialization phase during which random bits are distributed among the players, it is possible to perform each of k XOR computations using 2-rounds of communication. In each phase the random bits are used according to a cover-free family and this allows to use each random bit for more than one computation. For t = 2, we design a protocol that uses O(n log k) random bits instead of O(nk) bits if no recycling is performed. More generally, if t 1 then O(kt2 log n) random bits are sufficient to accomplisht his task, for t = O(n1/2-Ɛ) for constant Ɛ 0.