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Security Against Related Randomness Attacks via Reconstructive Extractors

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Cryptography and Coding (IMACC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 9496))

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Abstract

This paper revisits related randomness attacks against public key encryption schemes as introduced by Paterson, Schuldt and Sibborn (PKC 2014). We present a general transform achieving security for public key encryption in the related randomness setting using as input any secure public key encryption scheme in combination with an auxiliary-input reconstructive extractor. Specifically, we achieve security in the function-vector model introduced by Paterson et al., obtaining the first constructions providing CCA security in this setting. We consider instantiations of our transform using the Goldreich-Levin extractor; these outperform the previous constructions in terms of public-key size and reduction tightness, as well as enjoying CCA security. Finally, we also point out that our approach leads to an elegant construction for Correlation Input Secure hash functions, which have proven to be a versatile tool in diverse areas of cryptography.

The first and third authors were supported by EPSRC grant EP/L018543/1, the second author is supported by JSPS KAKENHI Grant Number 15K16006, and the last author is partially supported by ANR Project EnBiD (ANR-14-CE28-0003).

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Notes

  1. 1.

    See also [22] for an extended discussion of the practical motivation for studying related randomness attacks based on the attack literature as represented by [2, 6, 7, 9, 11–13, 15–17, 19, 21, 25].

  2. 2.

    Specifically, Wichs’ results apply to encryption schemes which are injective with respect to the used randomness.

  3. 3.

    The bound quoted in [10] had the denominator \(512 n p^2\). However, we believe the bound has a slight error and should in fact be \(512 n p^3\), as given here. The bound in Eq. (1) was also used by Paterson et al. in [23].

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Authors and Affiliations

  1. Royal Holloway, University of London, Surrey, UK

    Kenneth G. Paterson & Dale L. Sibborn

  2. National Institute of Advanced Industrial Science and Technology, Tokyo, Japan

    Jacob C. N. Schuldt

  3. École Normale Supérieure, Paris, France

    Hoeteck Wee

Authors
  1. Kenneth G. Paterson
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  2. Jacob C. N. Schuldt
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  3. Dale L. Sibborn
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  4. Hoeteck Wee
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Corresponding author

Correspondence to Jacob C. N. Schuldt .

Editor information

Editors and Affiliations

  1. University College London, Cambridge, United Kingdom

    Jens Groth

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Paterson, K.G., Schuldt, J.C.N., Sibborn, D.L., Wee, H. (2015). Security Against Related Randomness Attacks via Reconstructive Extractors. In: Groth, J. (eds) Cryptography and Coding. IMACC 2015. Lecture Notes in Computer Science(), vol 9496. Springer, Cham. https://doi.org/10.1007/978-3-319-27239-9_2

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  • DOI: https://doi.org/10.1007/978-3-319-27239-9_2

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