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International Conference on Provable Security

ProvSec 2014: Provable Security pp 162–177Cite as

Lossy Trapdoor Relation and Its Applications to Lossy Encryption and Adaptive Trapdoor Relation

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 8782))

Abstract

Peikert and Waters proposed the notion of lossy trapdoor function in STOC 2008. In this paper, we propose a relaxation of lossy trapdoor function, called lossy trapdoor relation. Unlike the lossy trapdoor function, lossy trapdoor relation does not require completely recovering the input but a public computable injective map of it. Interestingly, the lossy trapdoor relation maintains the application of lossy trapdoor function on the lossy encryption. Moreover, motivated by the construction of adaptive trapdoor relation proposed by Wee (Crypto 2010), we introduce all-but-one verifiable lossy trapdoor relation which is in fact a relaxation of all-but-one lossy trapdoor function.

  • The lossy trapdoor relation can be constructed from discrete logarithm related assumptions and subgroup membership assumptions efficiently. We also give an efficient construction of all-but-one verifiable lossy trapdoor relation from DLDH assumption over pairing group. As a byproduct, we propose an all-but-one lossy trapdoor function directly based on DLDH assumption which partially solve the open problem of Freeman et al. (PKC 2010).

  • The lossy trapdoor relation has a direct application to the lossy encryption and we propose new lossy encryptions based on three subgroup membership assumptions. The all-but-one verifiable lossy trapdoor relation can be used to construct adaptive trapdoor relation, which derives chosen ciphertext secure encryption.

Supported by the National Basic Research Program of China (973 project)(No.2013CB338002), the National Nature Science Foundation of China (No.61070171, No.61272534).

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Author information

Authors and Affiliations

  1. Data Assurance and Communication Security Research Center, Chinese Academy of Sciences, Beijing, China

    Haiyang Xue, Xianhui Lu, Bao Li & Yamin Liu

  2. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China

    Haiyang Xue, Xianhui Lu, Bao Li & Yamin Liu

  3. University of Chinese Academy of Sciences, Beijing, China

    Haiyang Xue

Authors
  1. Haiyang Xue
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  2. Xianhui Lu
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  3. Bao Li
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  4. Yamin Liu
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Editor information

Editors and Affiliations

  1. Department of Information Engineering, Chinese University of Hong Kong, Rm. 808 Ho Sin Hang Engineering Building, Sha Tin, N.T., Hong Kong

    Sherman S. M. Chow

  2. Institute for Infocomm Research, A*STAR, 1 Fusionopolis Way, 138632, Singapore, Singapore

    Joseph K. Liu

  3. Department of Computer Science, The University of Hong Kong, Chow Yei Ching Building, Pokfulam Road,, Hong Kong

    Lucas C. K. Hui

  4. Department of Computer Science, The University of Hong Kong, Chow Yei Ching Building, Pokfulam Road, Hong Kong

    Siu Ming Yiu

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© 2014 Springer International Publishing Switzerland

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Xue, H., Lu, X., Li, B., Liu, Y. (2014). Lossy Trapdoor Relation and Its Applications to Lossy Encryption and Adaptive Trapdoor Relation. In: Chow, S.S.M., Liu, J.K., Hui, L.C.K., Yiu, S.M. (eds) Provable Security. ProvSec 2014. Lecture Notes in Computer Science, vol 8782. Springer, Cham. https://doi.org/10.1007/978-3-319-12475-9_12

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  • DOI: https://doi.org/10.1007/978-3-319-12475-9_12

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-12474-2

  • Online ISBN: 978-3-319-12475-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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