All Complete Functionalities are Reversible

Crepeau and Santha, in 1991, posed the question of reversibility of functionalities, that is, which functionalities when used in one direction, could securely implement the identical functionality in the reverse direction. Wolf and Wullschleger, in 2006, showed that oblivious transfer is reversible. We study the problem of reversibility among 2-party SFE functionalities, which also enable general multi-party computation, in the information-theoretic setting. We show that any functionality that enables general multi-party computation, when used in both directions, is reversible. In fact, we show that any such functionality can securely realize oblivious transfer when used in an a priori fixed direction. This result enables secure computation using physical setups that parties can only use in a particular direction due to inherent asymmetries in them.

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