Abstract
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 in- stead of O(nk) bits if no recycling is performed. More generally, if t > 1 then O(kt 2 log n) random bits are sufficient to accomplisht his task, for t = O(n ½—є) for constant є > 0 .
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© 1999 Springer-Verlag Berlin Heidelberg
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Blundo, C., Galdi, C., Persiano, P. (1999). Randomness Recycling in Constant-Round Private Computations. In: Jayanti, P. (eds) Distributed Computing. DISC 1999. Lecture Notes in Computer Science, vol 1693. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48169-9_10
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DOI: https://doi.org/10.1007/3-540-48169-9_10
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