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Field Lifting for Smaller UOV Public Keys

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Progress in Cryptology – INDOCRYPT 2017 (INDOCRYPT 2017)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 10698))

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Abstract

Most Multivariate Quadratic (MQ) signature schemes have a very large public key, which makes them unsuitable for many applications, despite attractive features such as speed and small signature sizes. In this paper we introduce a modification of the Unbalanced Oil and Vinegar (UOV) signature scheme that has public keys which are an order of magnitude smaller than other MQ signature schemes. The main idea is to choose UOV keys over the smallest field \(\mathbb {F}_2\) in order to achieve small keys, but to lift the keys to a large extension field, where solving the MQ problem is harder. The resulting Lifted UOV signature scheme is very competitive with other post-quantum signature schemes in terms of key sizes, signature sizes and speed.

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Notes

  1. 1.

    However it is not a very good name because in reality oil mixes with oil and vinegar mixes with vinegar but no mixing happens between oil and vinegar, and this is not what happens in UOV polynomials. A better name would have been hen variables and rooster variables because hens can get along with hens and roosters, but two roosters start a fight when they appear in the same term. Moreover, this foreshadows the fact that in order for the signature scheme to be secure, the number of hen (vinegar) variables should be larger than the number of rooster (oil) variables. Nevertheless, we will stick to the traditional naming of oil and vinegar variables.

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Acknowledgements

This work was supported in part by the Research Council KU Leuven: C16/15/058. In addition, this work was supported by the European Commission through the Horizon 2020 research and innovation programme under grant agreement No. H2020-ICT-2014-644371 WITDOM and H2020-ICT-2014-645622 PQCRYPTO.

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  1. imec-COSIC KU Leuven, Kasteelpark Arenberg 10 - bus 2452, 3001, Heverlee, Belgium

    Ward Beullens & Bart Preneel

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  1. Ward Beullens
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Correspondence to Ward Beullens .

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Editors and Affiliations

  1. Indian Institute of Science (IISc), Bengaluru, India

    Arpita Patra

  2. Department of Computer Science, University of Bristol, Bristol, United Kingdom

    Nigel P. Smart

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Beullens, W., Preneel, B. (2017). Field Lifting for Smaller UOV Public Keys. In: Patra, A., Smart, N. (eds) Progress in Cryptology – INDOCRYPT 2017. INDOCRYPT 2017. Lecture Notes in Computer Science(), vol 10698. Springer, Cham. https://doi.org/10.1007/978-3-319-71667-1_12

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  • DOI: https://doi.org/10.1007/978-3-319-71667-1_12

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