On Compressing Linearly Shared Correlations

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Compressing correlated randomness is a key component of secure computation protocols in the silent preprocessing model and has received significant attention in recent years. Most existing constructions target additive correlations, where the parties receive additive shares of a relation. Beyond additive correlations, much less is known: more general linear correlations can be compressed using pseudorandom secret sharing, generic constructions for richer linear-output correlations can be obtaine