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Key Recovery Attacks Against NTRU-Based Somewhat Homomorphic Encryption Schemes

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Information Security (ISC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 9290))

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Abstract

A key recovery attack allows an attacker to recover the private key of an underlying encryption scheme when given a number of decryption oracle accesses. Previous research has shown that most existing Somewhat Homomorphic Encryption (SHE) schemes suffer from this attack. In this paper, we propose efficient key recovery attacks against two NTRU-based SHE schemes due to Lopez-Alt et al. (2012) and Bos et al. (2013), which have not gained much attention in the literature. Parallel to our work, Dahab, Galbraith and Morais (2015) have also proposed similar attacks but only for specific parameter settings. In comparison, our attacks apply to all parameter settings and are more efficient.

This paper is an extended abstract of the IACR report [CT15].

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Acknowledgements

Massimo Chenal is supported by an AFR Ph.D. grant from the National Research Fund, Luxembourg. Qiang Tang is partially supported by a CORE (junior track) grant from the National Research Fund, Luxembourg. We thank the IACR ePrint editors for pointing out references for three papers on key recovery attack against NTRUEncrypt and Steven Galbraith for valuable discussions.

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Authors and Affiliations

  1. APSIA Group, SnT, University of Luxembourg, 6 rue Richard Coudenhove-Kalergi, 1359, Luxembourg, Luxembourg

    Massimo Chenal & Qiang Tang

Authors
  1. Massimo Chenal
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  2. Qiang Tang
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Correspondence to Massimo Chenal .

Editor information

Editors and Affiliations

  1. University of Malaga, Malaga, Spain

    Javier Lopez

  2. Royal Holloway University of London, Egham, United Kingdom

    Chris J. Mitchell

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Chenal, M., Tang, Q. (2015). Key Recovery Attacks Against NTRU-Based Somewhat Homomorphic Encryption Schemes. In: Lopez, J., Mitchell, C. (eds) Information Security. ISC 2015. Lecture Notes in Computer Science(), vol 9290. Springer, Cham. https://doi.org/10.1007/978-3-319-23318-5_22

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  • DOI: https://doi.org/10.1007/978-3-319-23318-5_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23317-8

  • Online ISBN: 978-3-319-23318-5

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