Abstract
At FOCS 2002, a new generalized compact Knapsacks problem is introduced. It is shown that solving the generalized compact Knapsack problem on the average is at least as hard as the worst-case instance of various approximation problems over cyclic lattices. It is left as an open problem to construct a zero-knowledge proof of generalized compact Knapsack problem. In this paper, by investigating a new notion of one-way ensemble pair, we propose a generic construction of identification and achieve a signature with the Fiat-Shamir transformation. Following our generic construction, we implement a concrete scheme based on the random generalized compact Knapsack problem. Our scheme also implies the first efficient zero-knowledge proof of the generalized compact Knapsacks problem and results in a positive solution to the open problem at FOCS 2002.
This work is supported by ARC Discovery Grant DP0557493, the National Natural Science Foundation of China (No. 60403007) and the Project Foundation of Xi’an University of Technology in China (No. 108-210508).
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Qin, B., Wu, Q., Susilo, W., Mu, Y., Wang, Y. (2006). Zero-Knowledge Proof of Generalized Compact Knapsacks (or A Novel Identification/Signature Scheme). In: Yang, L.T., Jin, H., Ma, J., Ungerer, T. (eds) Autonomic and Trusted Computing. ATC 2006. Lecture Notes in Computer Science, vol 4158. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11839569_52
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DOI: https://doi.org/10.1007/11839569_52
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