(t,n) multi-secret sharing scheme extended from Harn-Hsu’s scheme

Abstract

Multi-secret sharing scheme has been well studied in recent years. In most multi-secret sharing schemes, all secrets must be recovered synchronously; the shares cannot be reused any more. In 2017, Harn and Hsu proposed a novel and reasonable feature in multiple secret sharing, such that the multiple secrets should be reconstructed asynchronously and the recovering of previous secrets do not leak any information on unrecovered secrets. Harn and Hsu also proposed a (t, n) multi-secret sharing scheme that satisfies this feature. However, the analysis on Harn-Hsu's scheme is wrong, and their scheme fails to satisfy this feature. If one secret is reconstructed, all the other unrecovered secrets can be computed by any t − 1 shareholders illegitimately. Another problem in Harn-Hsu's work is that the parameters are unreasonable which will be shown as follows. In this paper, we prove the incorrectness of Harn-Hsu's scheme and propose a new (t, n) multi-secret sharing scheme which is extended from Harn-Hsu's scheme; our proposed scheme satisfies the feature introduced by Harn and Hsu.

A novel authentication scheme for group based communication for IoT oriented infrastructure in smart cities

“…Furthermore, their scheme's parameters are also unreasonable. [30]. The present scheme is proposed to overcome the above-discussed outcomes and match the constraints specification of the IoT devices in grouped communication.…”

Protected Fair Secret Sharing Based Bivariate Asymmetric Polynomials in Satellite Network

“…The PVS-MSS scheme's main parameters, characteristics, and cost are compared with existing schemes. Compared with synchronous multi-secret sharing schemes such as [21,[28][29][30][31], the PVS-MSS scheme introduces verifiability. There is no need to maintain an additional secure channel between the ground control center and participants.…”

“…At present, verifiable secret sharing schemes based on bivariate polynomial design are all single secret sharing schemes [19]; Secondly, the primary purpose of the design is to construct an efficient verifiable secret sharing protocol in the presence of different numbers of cheaters. Research status of secret sharing scheme based on bivariate polynomial design: PSS scheme lacks various additional attributes to resist separate spoofing attacks and is suitable for different scenarios [20]; Reference [21,22], a simple multi-secret sharing scheme, can't resist the invasion of semi-honest people; The Verifiable Multi-Secret Sharing (VMSS) in reference [23] has no protected characteristics. The primary purpose of this scheme research is the verifiable attribute introduced into a secret sharing scheme with protected features like the PSS scheme.…”