Cryptography with One-Way Communication

There is a large body of work on using noisy communication channels for realizing different cryptographic tasks. In particular, it is known that secure message transmission can be achieved unconditionally using only one-way communication from the sender to the receiver. In contrast, known solutions for more general secure computation tasks inherently require interaction, even when the entire input originates from the sender. We initiate a general study of cryptographic protocols over noisy channels in a setting where only one party speaks. In this setting, we show that the landscape of what a channel is useful for is much richer. Concretely, we obtain the following results.