Skip to main content

Efficient Parallel Evaluation of Multivariate Quadratic Polynomials on GPUs

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNSC,volume 7690)

Abstract

QUAD is a provably secure stream cipher, whose security is based on the hardness assumption of solving multivariate quadratic polynomial systems over a finite field, which is known to be NP-complete. However, such provable security comes at a price, and QUAD is slower than most other stream ciphers that do not have security proofs.

In this paper, we discuss two efficient parallelization techniques for evaluating multivariate quadratic polynomial systems on GPU, which can effectively accelerate the QUAD stream cipher. The first approach focuses on formula of summations in quadratics, while the second approach uses parallel reduction to summations. Our approaches can be easily generalized and applied to other multivariate cryptosystems.

Keywords

  • Stream cipher
  • efficient implementation
  • multivariate cryptography
  • GPGPU

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bard, G.V.: Algebraic Cryptranalysis. Springer (2009)

    Google Scholar 

  2. Berbain, C., Billet, O., Gilbert, H.: Efficient Implementations of Multivariate Quadratic Systems. In: Biham, E., Youssef, A.M. (eds.) SAC 2006. LNCS, vol. 4356, pp. 174–187. Springer, Heidelberg (2007)

    CrossRef  Google Scholar 

  3. Berbain, C., Gilbert, H., Patarin, J.: QUAD: A Practical Stream Cipher with Provable Security. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 109–128. Springer, Heidelberg (2006)

    CrossRef  Google Scholar 

  4. Bonenberger, D., Krone, M.: Factorization of RSA-170, http://public.rz.fh-wolfenbuettel.de/~kronema/pdf/rsa170.pdf

  5. Chen, M.-S., Chen, T.-R., Cheng, C.-M., Hsiao, C.-H., Niederhagen, R., Yang, B.-Y.: What price a provably secure stream cipher? In: Fast Software Encryption, 2010, Rump session (2010)

    Google Scholar 

  6. Liu, F.-H., Lu, C.-J., Yang, B.-Y.: Secure PRNGs from Specialized Polynomial Maps over Any \(\mathbb{F}_{q}\). In: Buchmann, J., Ding, J. (eds.) PQCrypto 2008. LNCS, vol. 5299, pp. 181–202. Springer, Heidelberg (2008)

    CrossRef  Google Scholar 

  7. Manavski, S.: CUDA compatible GPU as an efficient hardware accelerator for AES cryptography. In: 2007 IEEE International Conference on Signal Processing and Communications, pp. 65–68 (2007)

    Google Scholar 

  8. NVIDIA CUDA, http://developer.NVIDIA.com/object/CUDA.html

  9. Osvik, D.A., Bos, J.W., Stefan, D., Canright, D.: Fast Software AES Encryption. In: Hong, S., Iwata, T. (eds.) FSE 2010. LNCS, vol. 6147, pp. 75–93. Springer, Heidelberg (2010)

    CrossRef  Google Scholar 

  10. Patarin, J., Goubin, L.: Asymmetric cryptography with s-boxes. In: First International Conference on Information and Communication Security, pp. 369–380 (1997)

    Google Scholar 

  11. Yang, B.-Y., Chen, O.C.-H., Bernstein, D.J., Chen, J.-M.: Analysis of QUAD. In: Biryukov, A. (ed.) FSE 2007. LNCS, vol. 4593, pp. 290–308. Springer, Heidelberg (2007)

    CrossRef  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Tanaka, S., Chou, T., Yang, BY., Cheng, CM., Sakurai, K. (2012). Efficient Parallel Evaluation of Multivariate Quadratic Polynomials on GPUs. In: Lee, D.H., Yung, M. (eds) Information Security Applications. WISA 2012. Lecture Notes in Computer Science, vol 7690. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35416-8_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-35416-8_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35415-1

  • Online ISBN: 978-3-642-35416-8

  • eBook Packages: Computer ScienceComputer Science (R0)