Lattice-Based Threshold Changeability for Standard Shamir Secret-Sharing Schemes

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> We consider the problem of increasing the threshold parameter of a secret-sharing scheme after the setup (share distribution) phase, without further communication between the dealer and the shareholders. Previous solutions to this problem require one to start off with a nonstandard scheme designed specifically for this purpose, or to have communication between shareholders. In contrast, we show how to increase the threshold parameter of the <emphasis emphasistype="italic">standard</emphasis> Shamir secret-sharing scheme without communication between the shareholders. Our technique can thus be applied to existing Shamir schemes even if they were set up without consideration to future threshold increases. </para>