HMFEv - An Efficient Multivariate Signature Scheme

Albrecht Petzoldt National Institute for Standards and Technology, Gaithersburg, MD, USA Ming-Shing Chen Academia Sinica, Taipei, Taiwan Jintai Ding University of Cincinnati, Ohio, USA Bo-Yin Yang Academia Sinica, Taipei, Taiwan

TBD mathscidoc:2207.43074

PQCrypto 2017, 205–223, 2017.6
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.
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  title={HMFEv - An Efficient Multivariate Signature Scheme},
  author={Albrecht Petzoldt, Ming-Shing Chen, Jintai Ding, and Bo-Yin Yang},
  booktitle={PQCrypto 2017},
Albrecht Petzoldt, Ming-Shing Chen, Jintai Ding, and Bo-Yin Yang. HMFEv - An Efficient Multivariate Signature Scheme. 2017. In PQCrypto 2017. pp.205–223.
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