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Compact Lossy and All-but-One Trapdoor Functions from Lattice

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Information Security Practice and Experience (ISPEC 2017)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 10701))

Abstract

Lossy trapdoor functions (LTDF) and all-but-one trapdoor functions (ABO-TDF) are fundamental cryptographic primitives. And given the recent advances in quantum computing, it would be much desirable to develop new and improved lattice-based LTDF and ABO-TDF. In this work, we provide more compact constructions of LTDF and ABO-TDF based on the learning with errors (LWE) problem. In addition, our LWE-based ABO-TDF can allow smaller system parameters to support super-polynomially many injective branches in the construction of CCA secure public key encryption. As a core building tool, we provide a more compact homomorphic symmetric encryption schemes based on LWE, which might be of independent interest. To further optimize the ABO-TDF construction, we employ the full rank difference encoding technique. As a consequence, the results presented in this work can substantially improve the performance of all the previous LWE-based cryptographic constructions based upon LTDF and ABO-TDF.

This research was supported in part by NSFC (Grant Nos. 61472084 and U1536205), National Key R&D Program of China (No. 2017YFB0802000), Shanghai innovation action project No. 16DZ1100200, and Shanghai science and technology development funds No. 16JC1400801.

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Authors and Affiliations

  1. School of Mathematical Sciences, Fudan University, Shanghai, China

    Leixiao Cheng & Quanshui Wu

  2. School of Computer Science, Fudan University, Shanghai, China

    Yunlei Zhao

Authors
  1. Leixiao Cheng
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  2. Quanshui Wu
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  3. Yunlei Zhao
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Correspondence to Yunlei Zhao .

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Editors and Affiliations

  1. Monash University, Clayton, Victoria, Australia

    Joseph K. Liu

  2. University of Milan, Milan, Italy

    Pierangela Samarati

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Cheng, L., Wu, Q., Zhao, Y. (2017). Compact Lossy and All-but-One Trapdoor Functions from Lattice. In: Liu, J., Samarati, P. (eds) Information Security Practice and Experience. ISPEC 2017. Lecture Notes in Computer Science(), vol 10701. Springer, Cham. https://doi.org/10.1007/978-3-319-72359-4_16

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  • DOI: https://doi.org/10.1007/978-3-319-72359-4_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-72358-7

  • Online ISBN: 978-3-319-72359-4

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