Abstract
In threshold encryption, the secret key is shared among a set of decryption parties, so that only a quorum of these parties can decrypt a given ciphertext. It is a useful building block in cryptology to distribute the trust of the secret key as well as increase availability. In particular, threshold Paillier encryption has been widely used in various security protocols, such as e-auction, e-voting and e-lottery. In this paper, we present the idea of designing provably secure threshold Paillier encryption using hyperplane geometry. Compared with the existing schemes that are based on polynomial interpolation, our work not only renovates the threshold Paillier cryptosystem using a different mathematical structure, but also enjoys some additional benefits: (1) our proposed method avoids the technical obstacle of computing inverses in the group whose order is unknown; (2) it gains computational advantages over Shoup’s trick and it can be used as a general building block to design secure and efficient threshold cryptosystems based on factoring.
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Acknowledgement
This work was partially supported by the National Natural Science Foundation of China (Grant No. 61501333, 61572379, 61370224), National Key Technology Support Program of China (Grant No. 2012BAH45B01), and Natural Science Foundation of Hubei Province of China (Grant No. 2015CFA069, 2015CFB257). We are also grateful to the anonymous reviewers for their valuable comments on the paper.
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Xia, Z., Yang, X., Xiao, M., He, D. (2016). Provably Secure Threshold Paillier Encryption Based on Hyperplane Geometry. In: Liu, J., Steinfeld, R. (eds) Information Security and Privacy. ACISP 2016. Lecture Notes in Computer Science(), vol 9723. Springer, Cham. https://doi.org/10.1007/978-3-319-40367-0_5
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DOI: https://doi.org/10.1007/978-3-319-40367-0_5
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