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International Conference on Applied Cryptography and Network Security

ACNS 2019: Applied Cryptography and Network Security Workshops pp 172–191Cite as

Strong Leakage Resilient Encryption by Hiding Partial Ciphertext

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11605))

Abstract

Leakage-resilient encryption is a powerful tool to protect data confidentiality against side channel attacks. In this work, we introduce a new and strong leakage setting to counter backdoor (or Trojan horse) plus covert channel attack, by relaxing the restrictions on leakage. We allow bounded leakage at anytime and anywhere and over anything. Our leakage threshold (e.g. 10000 bits) could be much larger than typical secret key (e.g. AES key or RSA private key) size. Under such a strong leakage setting, we propose an efficient encryption scheme which is semantic secure in standard setting (i.e. without leakage) and can tolerate strong continuous leakage. We manage to construct such a secure scheme under strong leakage setting, by hiding partial (e.g. 1%) ciphertext as secure as we hide the secret key using a small amount of more secure hardware resource, so that it is almost equally difficult for any adversary to steal information regarding this well-protected partial ciphertext or the secret key. We remark that, the size of such well-protected small portion of ciphertext is chosen to be much larger than the leakage threshold. We provide concrete and practical examples of such more secure hardware resource for data communication and data storage. Furthermore, we also introduce a new notion of computational entropy, as a sort of computational version of Kolmogorov complexity. Our quantitative analysis shows that, hiding partial ciphertext is a powerful countermeasure, which enables us to achieve higher security level than existing approaches in case of backdoor plus covert channel attacks. We also show the relationship between our new notion of computational entropy and existing relevant concepts, including All-or-Nothing Transform and Exposure Resilient Function. This new computation entropy formulation may have independent interests.

A full version [28] is available at https://eprint.iacr.org/2018/846.

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Notes

  1. 1.

    https://en.wikipedia.org/wiki/Kleptography and https://en.wikipedia.org/wiki/Dual_EC_DRBG.

  2. 2.

    http://spectrum.ieee.org/semiconductors/design/stopping-hardware-Trojans-in-their-tracks.

  3. 3.

    The encryption scheme is length-preserving, and the size of ciphertext is equal to the size of plaintext.

  4. 4.

    Note: (1) Many cloud storage servers provide a certain amount (e.g. 15GB) of free cloud storage for individual users; (2) the cost of offline local storage should include not only hardware purchase cost but also hardware maintenance and storage cost (i.e. keep the harddisk drive in a proper physical environment for a long time).

  5. 5.

    Actually, the motivation of this work is to provide an extremely secure (informally, close to physically isolated network) communication method in this “virtually isolated network” [29]. Here we choose strong leakage resilience against potential backdoor as our formal definition of “extremely secure”.

  6. 6.

    Usually, it is assumed that the adversary has access to the ciphertext.

  7. 7.

    https://www.schneier.com/academic/blowfish/.

  8. 8.

    http://csrc.nist.gov/publications/nistpubs/800-67-Rev1/SP-800-67-Rev1.pdf.

  9. 9.

    Shannon-Entropy is information-theoretical. Both Yao-Entropy and Hill-Entropy are computational variants.

  10. 10.

    When all random coins are treated as a part of input, any probabilistic algorithm will become deterministic.

  11. 11.

    When all random coins are treated as a part of input, any probabilistic algorithm will become deterministic.

  12. 12.

    The reason behind the definition of \(\varsigma (\ell , \sigma )\) (i.e. Eq. 10) is explained with details in our full version of this paper. Informally speaking, some steal algorithm \({{\mathsf {S}}}(\ell )\) is able to convey almost \(\ell +1\) bits message to \(\mathsf {R}\) algorithm, since \(| \{ 0, 1 \}^{\le \ell } | \approx |\{ 0,1 \}^{\ell +1}|\). When the error bound \(\epsilon \ge 2^{-(\ell -1)}\), we do not care the difference between such “almost” \(\ell +1\) bits message and actual \(\ell +1\) bits message.

  13. 13.

    We remark that some of these cited leakage resilient cryptography works actually propose leakage resilient pseudorandom generator/functions, instead of an encryption scheme. These pseudorandom generator/functions can be converted into encryption scheme using classical methods. These resulting encryption schemes will be a poor steal-resilient encryption.

  14. 14.

    The matrix row/column index starts with either zero or one, makes no essential difference to the property of Vandermonde matrix.

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Acknowledgment

The first author is supported by the National Research Foundation, Prime Minister’s Office, Singapore under its Corporate Laboratory@University Scheme, National University of Singapore, and Singapore Telecommunications Ltd. The second author is supported by the National Research Foundation (NRF), Prime Minister’s Office, Singapore, under its National Cybersecurity R&D Programme (Award No. NRF2014NCR-NCR001-31) and administered by the National Cybersecurity R&D Directorate.

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Authors and Affiliations

  1. Singtel/Trustwave, Singapore, Singapore

    Jia Xu

  2. Singapore University of Technology and Design, Singapore, Singapore

    Jianying Zhou

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  1. Jia Xu
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Correspondence to Jia Xu .

Editor information

Editors and Affiliations

  1. Singapore University of Technology and Design, Singapore, Singapore

    Jianying Zhou

  2. Singapore Management University, Singapore, Singapore

    Robert Deng

  3. University of California, Irvine, USA

    Zhou Li

  4. Massry Center for Business, University at Albany-SUNY, Albany, NY, USA

    Suryadipta Majumdar

  5. Technical University of Denmark, Kongens Lyngby, Denmark

    Weizhi Meng

  6. Concordia University, Montreal, QC, Canada

    Lingyu Wang

  7. Chinese University of Hong Kong, Shatin, Hong Kong

    Kehuan Zhang

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Xu, J., Zhou, J. (2019). Strong Leakage Resilient Encryption by Hiding Partial Ciphertext. In: Zhou, J., et al. Applied Cryptography and Network Security Workshops. ACNS 2019. Lecture Notes in Computer Science(), vol 11605. Springer, Cham. https://doi.org/10.1007/978-3-030-29729-9_10

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  • DOI: https://doi.org/10.1007/978-3-030-29729-9_10

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-030-29729-9

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