## Cryptology ePrint Archive: Report 2021/1089

Threshold scheme to share a secret by means of sound ranging

Sergij V. Goncharov

Abstract: In this short note we consider the scheme to share a bitstring secret among $n$ parties such that any $m$ of them, cooperating, can reconstruct it, but any $m - 1$ of them cannot (a so-called $(m,n)$-threshold scheme). The scheme is based on the sound ranging problem, which is to determine the unknown position of the source and the unknown instant when it emitted the sound from known instants when the sound wave reached known sensors. The features are 1) shadows are computed not so much by the secret dealer, but rather by environment where the sound propagates, so the amount of computations performed by the dealer is $O(1)$ instead of $O(n)$ as $n \rightarrow \infty$, and 2) the dealer does not need to establish separate secure channel with each party. There are severe inherent drawbacks though.

Category / Keywords: cryptographic protocols / secret sharing, threshold scheme, sound ranging, TDOA