Abstract

We study the relationship between the number of rounds needed to repeatedly perform a private computation (i.e., where there are many sets of inputs sequentially given to the players on which the players must compute a function privately) and the overall randomness needed for this task. For the XOR function we show that, by re-using the same $\ell$ random bits, we can significantly speed up the round-complexity of each computation compared to what is achieved by the naive strategy of partitioning the $\ell$ random bits between the computations. Moreover, we prove that our protocols are optimal in the amount of randomness they require.

MSC codes

  1. 94A60
  2. 68Q99
  3. 68R99

Keywords

  1. private distributed computations
  2. randomness
  3. round-complexity
  4. amortization

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Published In

cover image SIAM Journal on Discrete Mathematics
SIAM Journal on Discrete Mathematics
Pages: 533 - 544
ISSN (online): 1095-7146

History

Published online: 1 August 2006

MSC codes

  1. 94A60
  2. 68Q99
  3. 68R99

Keywords

  1. private distributed computations
  2. randomness
  3. round-complexity
  4. amortization

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