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HMFEv - An Efficient Multivariate Signature Scheme



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


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 can be 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.
Conference Dates
June 26-28, 2017
Conference Location
Conference Title
PQCrypto 2017: The Eighth International Conference on Post-Quantum Cryptography


Post-Quantum Cryptography, Multivariate Cryptography, Signature Schemes, NIST competition


Petzoldt, A. , Chen, M. , Ding, J. and Yang, B. (2017), HMFEv - An Efficient Multivariate Signature Scheme, PQCrypto 2017: The Eighth International Conference on Post-Quantum Cryptography, Utrecht, -1, [online], (Accessed April 20, 2024)
Created June 28, 2017, Updated November 10, 2018