Paper 2021/518

How to Share and Own a Secret

Victor Ermolaev and Gamze Tillem

Abstract

Custodian service is a service safeguarding a firm's or individual's financial assets or secret information. Such services often present a user with security versus ownership dilemma. The user does not wish to pass full control over their asset to the custodian to facilitate safeguarding. A control sharing mechanism allowing the custodian to hold enough information and keeping the user as the owner of the asset is required. For the assets being secret information, cryptographic protocols addressing this dilemma are known as prepositioned secret sharing~(PSS) protocols. PSS schemes distinguish redundant ``common'' shares and specific ``activating'' shares controlling the very possibility of the secret information reconstruction. Usually, PSS schemes: 1) lack robustness with respect to the amount of ``common'' shares, i.e., a high redundancy degree in ``common'' enables them to reconstruct the secret without ``activation'', and 2) are inflexible in configuring the robustness of the ``activating'' shares, i.e., how many ``activating'' shares can be lost or stolen before the secret can be reconstructed. In this paper, we present a PSS addressing these shortcomings.