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MQQ-SIG

An Ultra-Fast and Provably CMA Resistant Digital Signature Scheme

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Trusted Systems (INTRUST 2011)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7222))

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Abstract

We present MQQ-SIG, a signature scheme based on “Multivariate Quadratic Quasigroups”. The MQQ-SIG signature scheme has a public key consisting of \(\frac{n}{2}\) quadratic polynomials in n variables where n = 160, 192, 224 or 256. Under the assumption that solving systems of \(\frac{n}{2}\) MQQ’s equations in n variables is as hard as solving systems of random quadratic equations, we prove that in the random oracle model our signature scheme is CMA (Chosen-Message Attack) resistant.

From efficiency point of view, the signing and verification processes of MQQ-SIG are three orders of magnitude faster than RSA or ECDSA. Compared with other MQ signing schemes, MQQ-SIG has both advantages and disadvantages. Advantages are that it has more than three times smaller private keys (from 401 to 593 bytes), and the signing process is an order of magnitude faster than other MQ schemes. That makes it very suitable for implementation in smart cards and other embedded systems. However, MQQ-SIG has a big public key (from 125 to 512 Kb) and it is not suitable for systems where the size of the public key has to be small.

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Author information

Authors and Affiliations

  1. Department of Telematics, The Norwegian University of Science and Technology (NTNU), O.S. Bragstads plass 2E, N-7491, Trondheim, Norway

    Danilo Gligoroski

  2. Centre for Quantifiable Quality of Service in Communication Systems, NTNU, O.S. Bragstads plass 2E, N-7491, Trondheim, Norway

    Rune Steinsmo Ødegård, Rune Erlend Jensen & Svein Johan Knapskog

  3. INRIA, Paris-Rocquencourt Center, SALSA Project, UPMC Univ. Paris 06, UMR 7606, LIP6, F-75005, Paris, France

    Ludovic Perret & Jean-Charles Faugère

  4. CNRS, UMR 7606, LIP6, F-75005, Paris, France

    Ludovic Perret & Jean-Charles Faugère

  5. Faculty of Natural Sciences and Mathematics, Institute of Informatics, “Ss Cyril and Methodius” University, P.O. Box 162, 1000, Skopje, Macedonia

    Smile Markovski

Authors
  1. Danilo Gligoroski
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  2. Rune Steinsmo Ødegård
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  3. Rune Erlend Jensen
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  4. Ludovic Perret
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  5. Jean-Charles Faugère
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  6. Svein Johan Knapskog
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  7. Smile Markovski
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Editor information

Editors and Affiliations

  1. Hewlett-Packard Laboratories, Long Down Avenue, BS34 8QZ, Stoke Gifford, Bristol, UK

    Liqun Chen

  2. Computer Science Department, Columbia University, Room 465, S.W. Mudd Building, 10027, New York, NY, USA

    Moti Yung

  3. Institute of Technology, Beijing Key Lab of Intelligent Information Technology, 100081, Beijing, China

    Liehuang Zhu

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Gligoroski, D. et al. (2012). MQQ-SIG. In: Chen, L., Yung, M., Zhu, L. (eds) Trusted Systems. INTRUST 2011. Lecture Notes in Computer Science, vol 7222. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32298-3_13

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  • DOI: https://doi.org/10.1007/978-3-642-32298-3_13

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