Abstract
In a secret-sharing scheme, the secret is shared among a set of shareholders, and it can be reconstructed if a quorum of these shareholders work together by releasing their secret shares. However, in many applications, it is undesirable for nonshareholders to learn the secret. In these cases, pairwise secure channels are needed among shareholders to exchange the shares. In other words, a shared key needs to be established between every pair of shareholders. But employing an additional key establishment protocol may make the secret-sharing schemes significantly more complicated. To solve this problem, we introduce a new type of secret-sharing, calledprotected secret-sharing(PSS), in which the shares possessed by shareholders not only can be used to reconstruct the original secret but also can be used to establish the shared keys between every pair of shareholders. Therefore, in the secret reconstruction phase, the recovered secret is only available to shareholders but not to nonshareholders. In this paper, an information theoretically secure PSS scheme is proposed, its security properties are analyzed, and its computational complexity is evaluated. Moreover, our proposed PSS scheme also can be applied to threshold cryptosystems to prevent nonshareholders from learning the output of the protocols.
Highlights
Secret-sharing schemes, first introduced by Shamir [1] and Blakley [2] in 1979, are very important techniques to ensure secrecy and availability of sensitive information
In a (t, n) threshold secret-sharing scheme, the secret is divided into n shares so that it can only be recovered with t or more than t shares, but fewer than t shares cannot reveal any information of the secret
In the past few decades, many secret-sharing schemes have been proposed in the literature, and three major approaches can be used to design them: Shamir’s approach [1] based on the univariate polynomial, Blakely’s approach [2] based on the hyperplane geometry, and Mignotte/AsmuthBloom approach [3, 4] based on the Chinese Remainder Theorem (CRT)
Summary
Secret-sharing schemes, first introduced by Shamir [1] and Blakley [2] in 1979, are very important techniques to ensure secrecy and availability of sensitive information. We use bivariate polynomials to propose a new type of secret-sharing scheme, called protected secretsharing (PSS), in which shareholders can use their shares to achieve two purposes simultaneously: one is to reconstruct the original secret and the other is to establish a shared key between every pair of shareholders. Using these shared keys, shareholders can build pairwise secure channels among them to exchange the shares in the secret reconstruction phase.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
