Abstract-An important subclass of secure multiparty computation is secure sampling: two parties output samples of a pair of jointly distributed random variables such that neither party learns more about the other party's output than what its own output reveals. The parties make use of a setup -correlated random variables with a different distribution -as well as unlimited noiseless communication. An upperbound on the rate of producing samples of a desired distribution from a given setup is presented. The region of tension developed in this paper measures how well the dependence between a pair of random variables can be resolved by a piece of common information. The bounds on rate are a consequence of a monotonicity property: a protocol between two parties can only lower the tension between their "views". Connections are drawn between the region of tension and the notion of common information. A generalization of the Gács-Körner common information, called the Assisted Common Information, which takes into account "almost common" information ignored by Gács-Körner common information is defined. The region of tension is shown to be related to the rate regions of both the Assisted Common Information and the Gray-Wyner systems (and, a fortiori, Wyner's common information).
The full-fledged notion of tension region was developed in REF .
Assisted Common Information with an Application to Secure Two-Party Sampling
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ArXiv
Computer Science Mathematics