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Correlated secret randomness is a useful resource for secure computation protocols, often enabling dramatic speedups compared to protocols in the plain model. This has motivated a line of work on identifying and securely generating useful correlations.

Different kinds of correlations can vary greatly in terms of usefulness and ease of generation. While there has been major progress on efficiently generating oblivious transfer (OT) correlations, other useful kinds of correlations are much more costly to generate. Thus, it is highly desirable to develop efficient techniques for securely converting copies of a given source correlation into copies of a given target correlation, especially when the former are cheaper to generate than the latter.

In this work, we initiate a systematic study of such conversions that only involve a single uni-directional message. We refer to such a conversion as a one-message secure reduction …