Weighted Multiple Secret Sharing

Sep 28, 2011

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Abstract

Secret sharing is important in information and network security and has broad applications in the real world. Since an elegant secret sharing mechanism was first proposed by Shamir in 1979 (also Blakley did the similar work then), many schemes have appeared in literature. These schemes deal with either single or multiple secrets and their shares have either the same weight or different weights. Weighted shares mean that different shares have different capabilities in recovering the secret(s) -- a more (less) weighted share needs fewer (more) other shares to recover the secret(s).

In this talk, we will first discuss two primary categories of (representative) methods implementing secret sharing: polynomial based, i.e., Shamir's scheme, and Chinese Remainder Theorem (CRT) based, i.e., Mignotte's scheme. Then we present a new CRT based weighted multiple secret sharing scheme, based on the identification of a direct relation between the length (i.e., the number of bits) and the weight of shares. The new scheme can also be naturally applied to other cases such as sharing a single secret with same-weight shares and is remarkably simple and easy to implement. Compared to both Shamir's scheme and Mignotte's scheme, the new scheme is more efficient than both schemes in share computation and more efficient than Shamir's scheme (and as efficient as Mignotte's scheme) in secret recovery. One prominent and unique advantage of the new scheme is that it admits non-whole number weights which the existing schemes have not offered. Thus, the sizes of shares can vary distantly in fine-tuned granularity to fit different requirements and constraints of various devices such as sensors, PDAs, cell phones, iPads and to allow the new scheme to apply to broader applications involving wireless/sensor networks and pervasive computing.