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HMFEv - An Efficient Multivariate Signature Scheme

  • Albrecht Petzoldt
  • Ming-Shing Chen
  • Jintai Ding
  • Bo-Yin Yang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10346)

Abstract

Multivariate Cryptography, as one of the main candidates for establishing post-quantum cryptosystems, provides strong, efficient and well-understood digital signature schemes such as UOV, Rainbow, and Gui. While Gui provides very short signatures, it is, for efficiency reasons, restricted to very small finite fields, which makes it hard to scale it to higher levels of security and leads to large key sizes.

In this paper we propose a signature scheme called HMFEv (“Hidden Medium Field Equations”), which can be seen as a multivariate version of HFEv. We obtain our scheme by applying the Vinegar Variation to the MultiHFE encryption scheme of Chen et al. We show both theoretically and by experiments that our new scheme is secure against direct and Rank attacks. In contrast to other schemes of the HFE family such as Gui, HMFEv can be defined over arbitrary base fields and therefore is much more efficient in terms of both performance and memory requirements. Our scheme is therefore a good candidate for the upcoming standardization of post-quantum signature schemes.

Keywords

Post-quantum cryptography Multivariate cryptography Signature schemes NIST call for proposals 

Notes

Acknowledgments

The third author is partially supported by NIST. The second and fourth authors would like to thank Academia Sinica for the second author’s Investigator Award and Taiwan’s Ministry of Science and Technology grant MoST-105-2923-E-001-003-MY3. We want to thank the anonymous reviewers for their valuable comments which helped to improve this paper.

Disclaimer. Certain algorithms and commercial products are identified in this paper to foster understanding. Such identification does not imply recommendation or endorsement by NIST, nor does it imply that the algorithms or products identified are necessarily the best available for the purpose.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Albrecht Petzoldt
    • 1
  • Ming-Shing Chen
    • 2
  • Jintai Ding
    • 3
  • Bo-Yin Yang
    • 2
  1. 1.National Institute for Standards and TechnologyGaithersburgUSA
  2. 2.Academia SinicaTaipeiTaiwan
  3. 3.University of CincinnatiOhioUSA

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