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

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.

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