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].
Full version of the paper can be found at http://eccc.hpi-web.de/report/2013/130/
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Braverman, M., Garg, A. (2014). Public vs Private Coin in Bounded-Round Information. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds) Automata, Languages, and Programming. ICALP 2014. Lecture Notes in Computer Science, vol 8572. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43948-7_42
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DOI: https://doi.org/10.1007/978-3-662-43948-7_42
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