Abstract
The idea of Zero-Knowledge Sets (ZKS) was firstly proposed by Micali, Rabin and Kilian. It allows the prover to commit to a secret set and then prove either “x ∈ S” or “\(x \not\in S\)” without revealing any more knowledge of the set S. Afterwards, R.Gennaro defined the concept of independence for ZKS and gave two tree-based constructions. In this paper, we define the independence property for ZKS in a more flexible way than the definition of Gennaro’s and prove that for ZKS, our independence implies non-malleability and vice versa. Then an independent ZKS scheme is constructed in an algebraic way by mapping values to unique primes, accumulating the set members and hiding the set. Comparing with the tree-based constructions: our scheme is more efficient while proving a value belongs (resp. not belongs) to the committed set; furthermore, the committed set is easier to update.
Supported by the National Natural Science Foundation of China (No.60673073), the National High-Tech Research and Development Plan of China (863 project) (No.2006AA01Z427) and the National Basic Research Program of China (973 project)(No.2007CB311201).
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Jing, W., Xu, H., Li, B. (2011). A New Efficient Construction for Non-Malleable Zero-Knowledge Sets. In: Chung, Y., Yung, M. (eds) Information Security Applications. WISA 2010. Lecture Notes in Computer Science, vol 6513. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17955-6_3
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