HMFEv - An Efficient Multivariate Signature Scheme View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2017

AUTHORS

Albrecht Petzoldt , Ming-Shing Chen , Jintai Ding , Bo-Yin Yang

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. More... »

PAGES

205-223

References to SciGraph publications

  • 2013-10. Cryptanalysis of HFE, multi-HFE and variants for odd and even characteristic in DESIGNS, CODES AND CRYPTOGRAPHY
  • 2015. Design Principles for HFEv- Based Multivariate Signature Schemes in ADVANCES IN CRYPTOLOGY -- ASIACRYPT 2015
  • 2004. Theoretical Analysis of XL over Small Fields in INFORMATION SECURITY AND PRIVACY
  • 2009. SSE Implementation of Multivariate PKCs on Modern x86 CPUs in CRYPTOGRAPHIC HARDWARE AND EMBEDDED SYSTEMS - CHES 2009
  • 2001. QUARTZ, 128-Bit Long Digital Signatures in TOPICS IN CRYPTOLOGY — CT-RSA 2001
  • 2014. Differential Properties of the HFE Cryptosystem in POST-QUANTUM CRYPTOGRAPHY
  • 1999-04-15. Unbalanced Oil and Vinegar Signature Schemes in ADVANCES IN CRYPTOLOGY — EUROCRYPT ’99
  • 2016. On the Differential Security of the HFEv- Signature Primitive in POST-QUANTUM CRYPTOGRAPHY
  • 2013. Degree of Regularity for HFEv and HFEv- in POST-QUANTUM CRYPTOGRAPHY
  • 2008. Time-Area Optimized Public-Key Engines: $\mathcal{MQ}$ -Cryptosystems as Replacement for Elliptic Curves? in CRYPTOGRAPHIC HARDWARE AND EMBEDDED SYSTEMS – CHES 2008
  • 1999. Cryptanalysis of the HFE Public Key Cryptosystem by Relinearization in ADVANCES IN CRYPTOLOGY — CRYPTO’ 99
  • 2005. Rainbow, a New Multivariable Polynomial Signature Scheme in ROBOCUP 2005: ROBOT SOCCER WORLD CUP IX
  • 2011. Inverting HFE Systems Is Quasi-Polynomial for All Fields in ADVANCES IN CRYPTOLOGY – CRYPTO 2011
  • Book

    TITLE

    Post-Quantum Cryptography

    ISBN

    978-3-319-59878-9
    978-3-319-59879-6

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-319-59879-6_12

    DOI

    http://dx.doi.org/10.1007/978-3-319-59879-6_12

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1089973375


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