Skip to main content

Advertisement

Springer Nature Link
Log in
Menu
Find a journal Publish with us Track your research
Search
Cart
  1. Home
  2. Cryptographic Hardware and Embedded Systems – CHES 2012
  3. Conference paper

Efficient Implementations of MQPKS on Constrained Devices

  • Conference paper
  • pp 374–389
  • Cite this conference paper
Cryptographic Hardware and Embedded Systems – CHES 2012 (CHES 2012)
Efficient Implementations of MQPKS on Constrained Devices
  • Peter Czypek18,
  • Stefan Heyse18 &
  • Enrico Thomae18 

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7428))

Included in the following conference series:

  • International Workshop on Cryptographic Hardware and Embedded Systems
  • 5285 Accesses

  • 34 Citations

Abstract

Multivariate Quadratic Public Key Schemes (MQPKS) attracted the attention of researchers in the last decades for two reasons. First they are thought to resist attacks by quantum computers and second, most of the schemes were broken. The latter may be the reason why implementations are rare. This work investigates one of the most promising member of MQPKS and its variants, namely UOV, Rainbow and enTTS. UOV resisted all kinds of attacks for 13 years and can be considered one of the best examined MQPKS. We describe implementations of UOV, Rainbow and enTTS on an 8-bit microcontroller. To address the problem of large keys, we used several optimizations and also implemented the 0/1-UOV scheme introduced at CHES 2011. To achieve a practically usable security level on the selected device, all recent attacks are summarized and parameters for standard security levels are given. To allow judgement of scaling, the schemes are implemented for the most common security levels in embedded systems 264, 280 and 2128 bits symmetric security. This allows for the first time a direct comparison of the four schemes because they are implemented for exactly the same security levels on the same platform and also by the same developer.

Download to read the full chapter text

Chapter PDF

Similar content being viewed by others

A New Security Analysis Against MAYO and QR-UOV Using Rectangular MinRank Attack

Chapter © 2023

A New Fault Attack on UOV Multivariate Signature Scheme

Chapter © 2022

An Existential Unforgeable Signature Scheme Based on Multivariate Quadratic Equations

Chapter © 2017

Explore related subjects

Discover the latest articles, books and news in related subjects, suggested using machine learning.
  • Computational Complexity
  • Cryptology
  • Mobile and Network Security
  • Quantum Communications and Cryptography
  • Quantum Computing
  • Register-Transfer-Level Implementation

References

  1. Yang, B.-Y., Chen, J.-M., Chen, Y.-H.: TTS: High-Speed Signatures on a Low-Cost Smart Card. In: Joye, M., Quisquater, J.-J. (eds.) CHES 2004. LNCS, vol. 3156, pp. 371–385. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  2. Balasubramanian, S., Carter, H., Bogdanov, A., Rupp, A., Ding, J.: Fast Multivariate Signature Generation in Hardware: The Case of Rainbow. In: International Conference on Application-Specific Systems, Architectures and Processors, ASAP 2008, pp. 25–30 (July 2008)

    Google Scholar 

  3. Bettale, L., Faugère, J.-C., Perret, L.: Hybrid Approach for Solving Multivariate Systems over Finite Fields. Journal of Mathematical Cryptology 3(3), 177–197 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bouillaguet, C., Fouque, P.-A., Macario-Rat, G.: Practical key-recovery for all possible parameters of SFLASH. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 667–685. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  5. Braeken, A., Wolf, C., Preneel, B.: A Study of the Security of Unbalanced Oil and Vinegar Signature Schemes. In: Menezes, A. (ed.) CT-RSA 2005. LNCS, vol. 3376, pp. 29–43. Springer, Heidelberg (2005), http://eprint.iacr.org/2004/222/

    Chapter  Google Scholar 

  6. Buchmann, J., Ding, J. (eds.): PQCrypto 2008. LNCS, vol. 5299. Springer, Heidelberg (2008)

    MATH  Google Scholar 

  7. Faugère, J.-C., Joux, A.: Algebraic Cryptanalysis of Hidden Field Equation (HFE) Cryptosystems Using Gröbner Bases. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 44–60. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  8. Courtois, N.T., Daum, M., Felke, P.: On the Security of HFE, HFEv- and Quartz. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 337–350. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  9. Ding, J., Schmidt, D.: Rainbow, a New Multivariable Polynomial Signature Scheme. In: Ioannidis, J., Keromytis, A.D., Yung, M. (eds.) ACNS 2005. LNCS, vol. 3531, pp. 164–175. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  10. Driessen, B., Poschmann, A., Paar, C.: Comparison of Innovative Signature Algorithms for WSNs. In: Proceedings of ACM WiSec 2008. ACM (2008)

    Google Scholar 

  11. Garey, M.R., Johnson, D.S.: Computers and Intractability — A Guide to the Theory of NP-Completeness. W.H. Freeman and Company (1979) ISBN 0-7167-1044-7 or 0-7167-1045-5

    Google Scholar 

  12. Goubin, L., Courtois, N.T.: Cryptanalysis of the TTM Cryptosystem. In: Okamoto, T. (ed.) ASIACRYPT 2000. LNCS, vol. 1976, pp. 44–57. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  13. Gura, N., Patel, A., Wander, A., Eberle, H., Shantz, S.C.: Comparing Elliptic Curve Cryptography and RSA on 8-bit CPUs, pp. 119–132 (2004)

    Google Scholar 

  14. Kipnis, A., Patarin, J., Goubin, L.: Unbalanced Oil and Vinegar Signature Schemes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 206–222. Springer, Heidelberg (1999)

    Google Scholar 

  15. Kipnis, A., Shamir, A.: Cryptanalysis of the Oil and Vinegar Signature Scheme. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 257–266. Springer, Heidelberg (1998)

    Google Scholar 

  16. Kipnis, A., Shamir, A.: Cryptanalysis of the HFE Public Key Cryptosystem by Relinearization. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 19–30. Springer, Heidelberg (1999)

    Google Scholar 

  17. Patarin, J.: Cryptanalysis of the Matsumoto and Imai Public Key Scheme of Eurocrypt ’88. In: Coppersmith, D. (ed.) CRYPTO 1995. LNCS, vol. 963, pp. 248–261. Springer, Heidelberg (1995)

    Google Scholar 

  18. Petzoldt, A., Bulygin, S., Buchmann, J.: Selecting Parameters for the Rainbow Signature Scheme. In: Sendrier, N. (ed.) PQCrypto 2010. LNCS, vol. 6061, pp. 218–240. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  19. Petzoldt, A., Thomae, E., Bulygin, S., Wolf, C.: Small Public Keys and Fast Verification for \(\mathcal{M}\)ultivariate \(\mathcal{Q}\)uadratic Public Key Systems. In: Preneel, B., Takagi, T. (eds.) CHES 2011. LNCS, vol. 6917, pp. 475–490. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  20. Shor, P.W.: Polynomial-time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer. SIAM J. on Computing, 1484–1509 (1997)

    Google Scholar 

  21. Tang, S., Yi, H., Ding, J., Chen, H., Chen, G.: High-Speed Hardware Implementation of Rainbow Signature on FPGAs. In: Yang, B.-Y. (ed.) PQCrypto 2011. LNCS, vol. 7071, pp. 228–243. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  22. Thomae, E., Wolf, C.: Solving Underdetermined Systems of Multivariate Quadratic Equations Revisited. In: Fischlin, M., Buchmann, J., Manulis, M. (eds.) PKC 2012. LNCS, vol. 7293, pp. 156–171. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  23. Wolf, C., Braeken, A., Preneel, B.: Efficient Cryptanalysis of RSE(2)PKC and RSSE(2)PKC (2004)

    Google Scholar 

  24. Yang, B.-Y., Chen, J.-M.: Building Secure Tame-like Multivariate Public-Key Cryptosystems: The new TTS. In: Boyd, C., González Nieto, J.M. (eds.) ACISP 2005. LNCS, vol. 3574, pp. 518–531. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  25. Yang, B.-Y., Cheng, C.-M., Chen, B.-R., Chen, J.-M.: Implementing Minimized Multivariate PKC on Low-Resource Embedded Systems. In: Clark, J.A., Paige, R.F., Polack, F.A.C., Brooke, P.J. (eds.) SPC 2006. LNCS, vol. 3934, pp. 73–88. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Horst Görtz Institute for IT Security, Ruhr University Bochum, 44780, Bochum, Germany

    Peter Czypek, Stefan Heyse & Enrico Thomae

Authors
  1. Peter Czypek
    View author publications

    Search author on:PubMed Google Scholar

  2. Stefan Heyse
    View author publications

    Search author on:PubMed Google Scholar

  3. Enrico Thomae
    View author publications

    Search author on:PubMed Google Scholar

Editor information

Editors and Affiliations

  1. French Network and Information Security Agency (FNISA), 51 boulevard de La Tour-Maubourg, 75700, Paris, France

    Emmanuel Prouff

  2. The Bradley Department of Electrical and Computer Engineering, Virginia Polytechnic Institute, 302 Whittemore Hall, 24060, Blacksburg, VA, USA

    Patrick Schaumont

Rights and permissions

Reprints and permissions

Copyright information

© 2012 International Association for Cryptologic Research

About this paper

Cite this paper

Czypek, P., Heyse, S., Thomae, E. (2012). Efficient Implementations of MQPKS on Constrained Devices. In: Prouff, E., Schaumont, P. (eds) Cryptographic Hardware and Embedded Systems – CHES 2012. CHES 2012. Lecture Notes in Computer Science, vol 7428. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33027-8_22

Download citation

  • .RIS
  • .ENW
  • .BIB
  • DOI: https://doi.org/10.1007/978-3-642-33027-8_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33026-1

  • Online ISBN: 978-3-642-33027-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Share this paper

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • Multivariate Quadratic Signatures
  • MQ
  • Unbalanced Oil and Vinegar
  • UOV
  • Rainbow
  • enTTS
  • AVR
  • Embedded Device

Publish with us

Policies and ethics

Search

Navigation

  • Find a journal
  • Publish with us
  • Track your research

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Journal finder
  • Publish your research
  • Language editing
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our brands

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Discover
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support
  • Legal notice
  • Cancel contracts here

172.70.80.62

ICE Institution of Civil Engineers (3000167333) - Institution of Civil Engineers Library (2000027800)

Springer Nature

© 2025 Springer Nature