Public vs Private Coin in Bounded-Round Information

  • Mark Braverman
  • Ankit Garg
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8572)

Abstract

We precisely characterize the role of private randomness in the ability of Alice to send a message to Bob while minimizing the amount of information revealed to him. We give an example of a (randomized) message which can be transmitted while revealing only I bits of information using private randomness, but requires Alice to reveal I + logI − O(1) bits of information if only public coins are allowed. This gives the first example of an ω(1) additive separation between these two models. Our example also shows that the one-round compression construction of Harsha et al. [HJMR07] cannot be improved.

Moreover, we show that our example is tight up to an additive O(1) factor: We show that if using private randomness a message can be transmitted while revealing I bits of information, the transmission can be simulated without private coins using I + logI + O(1) bits of information. This improves over an earlier result by Brody et al. [BBK+12].

Keywords

Entropy Univer Weinstein 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Mark Braverman
    • 1
  • Ankit Garg
    • 1
  1. 1.Princeton UniversityUSA

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