High Entropy Random Selection Protocols

We study the two party problem of randomly selecting a string among all the strings of length n. We want the protocol to have the property that the output distribution has high entropy, even when one of the two parties is dishonest and deviates from the protocol. We develop protocols that achieve high, close to n, entropy. In the literature the randomness guarantee is usually expressed as being close to the uniform distribution or in terms of resiliency. The notion of entropy is not directly comparable to that of resiliency, but we establish a connection between the two that allows us to compare our protocols with the existing ones. We construct an explicit protocol that yields entropy n − O(1) and has 4 log∗ n rounds, improving over the protocol of Goldwasser et al. [3] that also achieves this entropy but needs O(n) rounds. Both these protocols need O(n2 ) bits of communication. Next we reduce the communication in our protocols. We show the existence, non-explicitly, of a protoco...

• Type: Conference
• Year: 2007
• Where: APPROX
• Authors: Harry Buhrman, Matthias Christandl, Michal Koucký, Zvi Lotker, Boaz Patt-Shamir, Nikolai K. Vereshchagin
• Keywords: Algorithms, APPROX 2007, Entropy, Explicit Protocols, Simple Explicit Protocols