On Secure Computation Over the Binary Modulo-2 Adder Multiple-Access Wiretap Channel

TL;DR

This paper introduces the secrecy computation-capacity for secure function computation over a binary modulo-2 adder multiple-access wiretap channel, showing that under certain conditions, it equals the non-secure computation capacity without extra randomness.

Contribution

It characterizes the secrecy computation-capacity for this channel and reveals conditions where secure computation matches the non-secure capacity, differing from message transmission scenarios.

Findings

Secrecy computation-capacity equals computation capacity under specific algebraic conditions.

No additional randomness or advantage is needed for secure computation in this setting.

Secure function computation can be fundamentally different from secure message transmission.

Abstract

In this paper, the problem of securely computing a function over the binary modulo-2 adder multiple-access wiretap channel is considered. The problem involves a legitimate receiver that wishes to reliably and efficiently compute a function of distributed binary sources while an eavesdropper has to be kept ignorant of them. In order to characterize the corresponding fundamental limit, the notion of secrecy computation-capacity is introduced. Although determining the secrecy computation-capacity is challenging for arbitrary functions, it surprisingly turns out that if the function perfectly matches the algebraic structure of the channel and the joint source distribution fulfills certain conditions, the secrecy computation-capacity equals the computation capacity, which is the supremum of all achievable computation rates without secrecy constraints. Unlike the case of securely transmitting messages, no additional randomness is needed at the encoders nor does the legitimate receiver need any advantage over the eavesdropper. The results therefore show that the problem of securely computing a function over a multiple-access wiretap channel may significantly differ from the one of securely communicating messages.