On the Fairness of Groce{Katz's Protocol for Rational Players

Abstract

In Eurocrypt 2012, Groce and Katz provided a mathematical description about `incentive compatible' setting in the context of fair two party computation with rational players. They showed, how by modifying the utility values, `incentive incompatible' setting can be converted into `incentive compatible' setting for an XOR function. In this paper, we try to understand, whether by modi cation of the utility values, `incentive incompatible' setting could always be converted into `incentive compatible' setting for any function. In this direction, we observe two distinct classes of functions which show `incentive incompatibility' for any value of utilities assuming certain guessing strategies and input distribution. One class includes all functions without an embedded XOR and other class has a speci c function containing an embedded XOR. Such functions had been used to show the rst fair two party secure computation with non-rational players (Gordon et al., STOC 2008). Our observations help to understand the structure of such `incentive incompatible' functions