Skip to main content

Secure Variants of the Square Encryption Scheme

  • Conference paper
Post-Quantum Cryptography (PQCrypto 2010)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 6061))

Included in the following conference series:

Abstract

This paper discusses two encryption schemes to fix the Square scheme. Square+ uses the Plus modification of appending randomly chosen polynomials. Double-Layer Square uses a construction similar to some signature schemes, splitting the variables into two layers, one of which depends on the other.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Baena, J., Clough, C., Ding, J.: Square-Vinegar Signature Scheme. In: Buchmann, J., Ding, J. (eds.) PQCrypto 2008. LNCS, vol. 5299, pp. 17–30. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  2. Billet, O., Gilles, M.-R.: Cryptanalysis of the Square Cryptosystems. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 451–468. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  3. Clough, C., Baena, J., Ding, J., Yang, B.-Y., Chen, M.: Square, a new multivariate encryption scheme. In: Fischlin, M. (ed.) CT-RSA 2009. LNCS, vol. 5473, pp. 252–264. Springer, Heidelberg (2009)

    Google Scholar 

  4. Courtois, N.: The security of hidden field equations (HFE). In: Naccache, D. (ed.) CT-RSA 2001. LNCS, vol. 2020, pp. 266–281. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  5. Ding, J., Dubois, V., Yang, B.-Y., Owen Chen, C.-H., Cheng Could, C.-M.: Could SFLASH be Repaired? In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part II. LNCS, vol. 5126, pp. 691–701. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  6. Ding, J., Gower, J.E., et al.: Inoculating Multivariate Schemes against differential attacks. In: Yung, M., Dodis, Y., Kiayias, A., Malkin, T.G. (eds.) PKC 2006. LNCS, vol. 3958, pp. 290–301. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  7. 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)

    Google Scholar 

  8. Ding, J., Schmidt, D., Werner, F.: Algebraic attack on HFE revisited. In: Wu, T.-C., Lei, C.-L., Rijmen, V., Lee, D.-T. (eds.) ISC 2008. LNCS, vol. 5222, pp. 215–227. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  9. Dubois, V., Granboulan, L., Stern, J.: An efficient provable distinguisher for HFE. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4052, pp. 156–167. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  10. Faugére, J.-C.: A new efficient algorithm for computing Gröbner bases \((F\sb 4)\). J. Pure Appl. Algebra 139(1-3), 61–88 (1999); Effective methods in algebraic geometry (Saint-Malo, 1998)

    Article  MATH  MathSciNet  Google Scholar 

  11. 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)

    Google Scholar 

  12. Jiang, X., Ding, J., Hu, L.: Public Key Analysis-Kipnis-Shamir Attack on HFE Revisited. In: Pei, D., Yung, M., Lin, D., Wu, C. (eds.) Inscrypt 2007. LNCS, vol. 4990, pp. 399–411. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  13. 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 

  14. Matsumoto, T., Imai, H.: Public quadratic polynomial-tuples for efficient signature-verification and message-encryption. In: Günther, C.G. (ed.) EUROCRYPT 1988. LNCS, vol. 330, pp. 419–453. Springer, Heidelberg (1988)

    Google Scholar 

  15. Mohamed, M.S.E., Mohamed, W., Ding, J., Buchmann, J.: MXL2: Solving Polynomial Equations over GF (2) Using an Improved Mutant Strategy. In: Buchmann, J., Ding, J. (eds.) PQCrypto 2008. LNCS, vol. 5299, pp. 203–215. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  16. Patarin, J.: Hidden Field Equations (HFE) and Isomorphisms of Polynomials (IP): Two new families of asymmetric algorithms. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 33–48. Springer, Heidelberg (1996)

    Google Scholar 

  17. Patarin, J., Goubin, L., Courtois, N.: C*-+ and HM: Variations around two schemes of T. Matsumoto and H. Imai. In: Ohta, K., Pei, D. (eds.) ASIACRYPT 1998. LNCS, vol. 1514, pp. 35–50. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Clough, C.L., Ding, J. (2010). Secure Variants of the Square Encryption Scheme. In: Sendrier, N. (eds) Post-Quantum Cryptography. PQCrypto 2010. Lecture Notes in Computer Science, vol 6061. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12929-2_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-12929-2_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-12928-5

  • Online ISBN: 978-3-642-12929-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics