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International Workshop on Security

IWSEC 2016: Advances in Information and Computer Security pp 289–304Cite as

On the Security and Key Generation of the ZHFE Encryption Scheme

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 9836))

Abstract

At PQCrypto’14 Porras, Baena and Ding proposed a new interesting construction to overcome the security weakness of the HFE encryption scheme, and called their new encryption scheme ZHFE. They provided experimental evidence for the security of ZHFE, and proposed the parameter set \((q,n,D)= (7,55,105)\) with claimed security level \(2^{80}\) estimated by experiment. However there is an important gap in the state-of-the-art cryptanalysis of ZHFE, i.e., a sound theoretical estimation for the security level of ZHFE is missing. In this paper we fill in this gap by computing upper bounds for the Q-Rank and for the degree of regularity of ZHFE in terms of \(\log _q D\), and thus providing such a theoretical estimation. For instance the security level of ZHFE(7,55,105) can now be estimated theoretically as at least \(2^{96}\). Moreover for the inefficient key generation of ZHFE, we also provide a solution to improve it significantly, making almost no computation needed.

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Acknowledgment

The authors would like to thank the anonymous reviewers of PQCrypto’16 for their valuable comments on an early version of this paper, and the anonymous reviewers of IWSEC’16 for their helpful comments on this paper.The first author would like to thank the financial support from the National Natural Science Foundation of China (Grant No. 61572189).

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Authors and Affiliations

  1. Temasek Laboratories, National University of Singapore, Singapore, Singapore

    Wenbin Zhang & Chik How Tan

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  1. Wenbin Zhang
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  2. Chik How Tan
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Correspondence to Wenbin Zhang .

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Editors and Affiliations

  1. Japan Broadcasting Corporation, Tokyo, Japan

    Kazuto Ogawa

  2. Yokohama National University, Yokohama, Japan

    Katsunari Yoshioka

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Zhang, W., Tan, C.H. (2016). On the Security and Key Generation of the ZHFE Encryption Scheme. In: Ogawa, K., Yoshioka, K. (eds) Advances in Information and Computer Security. IWSEC 2016. Lecture Notes in Computer Science(), vol 9836. Springer, Cham. https://doi.org/10.1007/978-3-319-44524-3_17

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  • DOI: https://doi.org/10.1007/978-3-319-44524-3_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-44523-6

  • Online ISBN: 978-3-319-44524-3

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