Publicly verifiable secret sharing scheme and its application with almost optimal information rate

Abstract

It is well known that the construction of publicly verifiable secret sharing scheme with high information rate is a challenge. The information rates of the existing schemes are generally less than one‐half; for this problem, we put forward a publicly verifiable secret sharing scheme with almost optimal information rate based on multilinear Diffie–Hellman assumption. First, we construct a knowledge commitment scheme by using multilinear map; on the basis of this scheme, we propose a publicly verifiable secret sharing scheme whose information rate is (m − 1)/m (The secret is (m − 1)‐dimensional vector), which is almost asymptotically optimal. Second, the public verifiability of the scheme is achieved by using the multiple linear property of a multilinear map. Again, under multilinear Diffie–Hellman assumption, we proved the security of our scheme. And we apply our publicly verifiable secret sharing scheme to public‐key encryption system skillfully. At last, the performance analysis results show the effectiveness and practicality of our scheme. Copyright © 2017 John Wiley & Sons, Ltd.

How to construct a verifiable multi‐secret sharing scheme based on graded encoding schemes

“…More precisely, the security of the proposed VMSS scheme is based on the GDDH problem. As we mentioned earlier, there have already been verifiable (multi)-secret sharing schemes based on multilinear maps (the maps which do not really exist) [2,31]. So our VMSS scheme is the first realisation of such verifiable schemes.…”

“…Here, we first propose a comparison of the basic properties in the new VMSS scheme with (t, n) threshold verifiable (multi)secret sharing schemes in the literature [2,31]. For easiness, the abbreviations S 1 and S 2 are used for our first and second schemes, respectively.…”

“…By multiple linear pairs, two (Publicly) VSS schemes were proposed by Peng and Tian [2,31]. These two schemes are based on multilinear maps and not on graded encoding schemes.…”

“…The VSS schemes [22,[24][25][26] are based on bilinear maps, which can be built from the pairing of elliptic curves. Also, there are VSS schemes such as [2,31] which have been constructed using multilinear maps (the maps which do not exist). On the other hand, all of the above-mentioned schemes, have (t, n) threshold access structures in which only any at least t participants can reconstruct the secret, while in general access structure the participants do not have the same ability to recover the secret.…”

“…In a multi-secret sharing (MSS) scheme, several secrets are distributed among a group of participants by a dealer D such that only authorised sets can reconstruct the secrets by combining their shares (or their pseudo shares), while other subsets cannot know any information about them [1]. For sharing the secrets, there are many techniques such as multilinear maps [2], polynomial interpolation [3,4], using the Chinese remainder theorem [5,6], monotone span program (MSP) [7,8] and so on. The notion of MSP which will be described later, was introduced by Karchmer and Wigdersonm [9].…”