Abstract
There is a lack of more complicated ideal-lattice-based cryptosystems which require the use of lattice trapdoors, for the reason that currently known trapdoors are either only applicable to general lattices or not well-studied in the ring setting. To facilitate the development of such cryptosystems, we extend the notion of lattice trapdoors of Micciancio and Peikert (Eurocrypt ’12) into the ring setting with careful justification. As a demonstration, we use the new trapdoor to construct a new hierarchical identity-based encryption scheme, which allows us to construct public-key encryption with chosen-ciphertext security, signatures, and public-key searchable encryption.
This work is supported by grants 439713, 14201914 from Research Grants Council (RGC), and grants 4055018, 4930034 from The Chinese University of Hong Kong. Sherman Chow is supported by the Early Career Award from RGC. Part of the work was done while the second author is with Department of Information Engineering.
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- 1.
We switch the notation from the original \(R\) in [12] to \(T\) to avoid clashing of notations in the later sections.
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Lai, R.W.F., Cheung, H.K.F., Chow, S.S.M. (2015). Trapdoors for Ideal Lattices with Applications. In: Lin, D., Yung, M., Zhou, J. (eds) Information Security and Cryptology. Inscrypt 2014. Lecture Notes in Computer Science(), vol 8957. Springer, Cham. https://doi.org/10.1007/978-3-319-16745-9_14
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