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n-Evasive all-but-many lossy trapdoor function and its constructions

Authors

  • Zhengan Huang,

    1. Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, China
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  • Shengli Liu,

    Corresponding author
    1. Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, China
    • Correspondence: Shengli Liu, Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China.

      E-mail: slliu@sjtu.edu.cn

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  • Kefei Chen

    1. School of Science, Hangzhou Normal University, Hangzhou, China
    2. State Key Laboratory of Mathematical Engineering and Advanced Computing, Wuxi, China
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Abstract

In this paper, we propose the notion of n-evasive all-but-many lossy trapdoor functions (ABM-LTFs), which is an extended abstraction of all-but-n lossy trapdoor functions (ABN-LTFs) proposed by Hemenway et al. in Asiacrypt 2011 and, at the same time, is a special case of ABM-LTFs proposed by Hofheinz in Eurocrypt 2012. We show two constructions of n-evasive ABM-LTFs. The first one is based on the decisional composite residuosity (DCR) assumption, and the second one is from chameleon hash functions and ABN-LTFs. Both of the constructions are based on reasonable assumptions with tight security reductions. Similar to ABN-LTFs and ABM-LTFs, n-evasive ABM-LTFs can be employed to construct indistinguishability-based selective opening chosen-ciphertext secure public-key encryption (PKE) schemes and may have other applications in cryptography. The instantiation of n-evasive ABM-LTFs can be based on the well-known assumption, for example, DCR, and the security reduction is much tighter than that of ABM-LTFs. On the other hand, the black-box PKE construction from n-evasive ABM-LTFs is more general than that from ABN-LTFs. Copyright © 2014 John Wiley & Sons, Ltd.

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