In this paper, we propose a new secret sharing scheme for secure multi-party computation. We present a general framework that allows us to construct efficient secret sharing schemes from channel coding techniques for the wiretap channel. The resulting schemes can be employed to securely calculate linear functions of data that are distributed in a network without leaking any information on the data except the desired result. For the examples considered in this paper, our schemes minimize the communication overhead while keeping the data perfectly secure. Compared to conventional schemes, for which the communication overhead grows quadratically in the number of clients in the considered scenarios, the communication overhead for our approach grows only linearly with the number of clients. This property is maintained even if our secret sharing scheme is set up to introduce redundancy in order to compensate for losses of secret shares. While we only consider the case of passive eavesdroppers and implementations based on nested Reed-Solomon codes in this paper, the proposed framework can also be applied in other cases (e.g., when clients tamper with the data) by taking into account the effects of attacks in the design of the underlying wiretap code.
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