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On the Differential Security of Multivariate Public Key Cryptosystems

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Post-Quantum Cryptography (PQCrypto 2011)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7071))

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Abstract

Since the discovery of an algorithm for factoring and computing discrete logarithms in polynomial time on a quantum computer, the cryptographic community has been searching for an alternative for security in the approaching post-quantum world. One excellent candidate is multivariate public key cryptography. Though the speed and parameterizable nature of such schemes is desirable, a standard metric for determining the security of a multivariate cryptosystem has been lacking. We present a reasonable measure for security against the common differential attacks and derive this measurement for several modern multivariate public key cryptosystems.

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References

  1. Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Sci. Stat. Comp. 26, 1484 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  2. Chen, A.I.-T., Chen, M.-S., Chen, T.-R., Cheng, C.-M., Ding, J., Kuo, E.L.-H., Lee, F.Y.-S., Yang, B.-Y.: SSE Implementation of Multivariate PKCs on Modern X86 CPUs. In: Clavier, C., Gaj, K. (eds.) CHES 2009. LNCS, vol. 5747, pp. 33–48. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  3. Chen, A.I.-T., Chen, C.-H.O., Chen, M.-S., Cheng, C.-M., Yang, B.-Y.: Practical-Sized Instances of Multivariate PKCs: Rainbow, TTS, and ℓIC-Derivatives. In: Buchmann, J., Ding, J. (eds.) PQCrypto 2008. LNCS, vol. 5299, pp. 95–108. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  4. 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 

  5. Clough, C., Baena, J., Ding, J., Yang, B.-Y., Chen, M.-s.: Square, a New Multivariate Encryption Scheme. In: Fischlin, M. (ed.) CT-RSA 2009. LNCS, vol. 5473, pp. 252–264. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  6. 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 

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

    Chapter  Google Scholar 

  8. Dubois, V., Fouque, P.-A., Shamir, A., Stern, J.: Practical Cryptanalysis of SFLASH. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 1–12. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

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

    Chapter  Google Scholar 

  10. Smith-Tone, D.: Properties of the Discrete Differential with Cryptographic Applications. In: Sendrier, N. (ed.) PQCrypto 2010. LNCS, vol. 6061, pp. 1–12. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  11. 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 

  12. 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)

    Chapter  Google Scholar 

  13. 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)

    Chapter  Google Scholar 

  14. Patarin, J.: The oil and vinegar algorithm for signatures. Presented at the Dagsthul Workshop on Cryptography (1997)

    Google Scholar 

  15. Ding, J., Dubois, V., Yang, B.Y., Chen, C.H.O., Cheng, 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 

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Louisville, Louisville, Kentucky, USA

    Daniel Smith-Tone

  2. National Institute of Standards and Technology, Gaithersburg, Maryland, USA

    Daniel Smith-Tone

Authors
  1. Daniel Smith-Tone
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Editor information

Editors and Affiliations

  1. Academia Sinica, Taipei, Taiwan

    Bo-Yin Yang

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Smith-Tone, D. (2011). On the Differential Security of Multivariate Public Key Cryptosystems. In: Yang, BY. (eds) Post-Quantum Cryptography. PQCrypto 2011. Lecture Notes in Computer Science, vol 7071. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25405-5_9

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  • DOI: https://doi.org/10.1007/978-3-642-25405-5_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25404-8

  • Online ISBN: 978-3-642-25405-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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