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|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].|
|Citation:||Braverman, Mark, and Ankit Garg. "Public vs Private Coin in Bounded-Round Information." Automata, Languages, and Programming (2014): pp. 502-513. doi:10.1007/978-3-662-43948-7_42|
|Pages:||502 - 513|
|Type of Material:||Conference Article|
|Series/Report no.:||Lecture Notes in Computer Science;|
|Journal/Proceeding Title:||Automata, Languages, and Programming|
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