Information-theoretic secret sharing from correlated Gaussian random variables and public communication

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Authors
Rana, Vidhi
Chou, Rémi
Kwon, Hyuck M.
Issue Date
2021
Type
Article
Language
en_US
Keywords
Secret sharing , Information-theoretic security , Rate-limited communication , Gaussian sources
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Abstract

Abstract—In this paper, we study an information-theoretic secret sharing problem, where a dealer distributes shares of a secret among a set of participants under the following constraints: (i) authorized sets of users can recover the secret by pooling their shares, and (ii) non-authorized sets of colluding users cannot learn any information about the secret. We assume that the dealer and participants observe the realizations of correlated Gaussian random variables and that the dealer can communicate with participants through a one-way, authenticated, rate-limited, and public channel. Unlike traditional secret sharing protocols, in our setting, no perfectly secure channel is needed between the dealer and the participants. Our main result is a closed-form characterization of the fundamental trade-off between secret rate and public communication rate.

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Citation
Rana, V., Chou, R. A., & Kwon, H. (2021). Information-theoretic secret sharing from correlated gaussian random variables and public communication. IEEE Transactions on Information Theory, doi:10.1109/TIT.2021.3122808
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IEEE
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ISSN
0018-9448
1557-9654
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