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)


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].


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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