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Cryptanalysis of Hash-Based Tamed Transformation and Minus Signature Scheme

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Post-Quantum Cryptography (PQCrypto 2013)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7932))

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Abstract

In 2011, wang et al. proposed a security enhancement method of Multivariate Public Key Cryptosystems (MPKCs), named Extended Multivariate public key Cryptosystems (EMC). They introduced more variables in an original MPKC by a so-called Hash-based Tamed (HT) transformation in order to resist existing attack on the original MPKC. They proposed Hash-based Tamed Transformation and Minus (HTTM) signature scheme which combined EMC method with minus method. Through our analysis, the HTTM is not secure as they declared. If we can forge a valid signature of the original MPKC-minus signature scheme, we could forge a valid signature of HTTM scheme successfully.

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References

  1. Courtois, N., Klimov, A., Patarin, J., Shamir, A.: Efficient algorithms for solving overdefined systems of multivariate polynomial equations. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 392–407. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  2. Ding, J.: A new variant of the Matsumoto-Imai cryptosystem through perturbation. In: Bao, F., Deng, R., Zhou, J. (eds.) PKC 2004. LNCS, vol. 2947, pp. 305–318. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  3. 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 

  4. Ding, J., Hu, L., Nie, X., Li, J., Wagner, J.: High Order Linearization Equation (HOLE) Attack on Multivariate Public Key Cryptosystems. In: Okamoto, T., Wang, X. (eds.) PKC 2007. LNCS, vol. 4450, pp. 233–248. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  5. Dubois, V., Fouque, P., 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 

  6. Fouque, P.-A., Granboulan, L., Stern, J.: Differential Cryptanalysis for Multivariate Schemes. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 341–353. Springer, Heidelberg (2005)

    Chapter  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. Garey, M., Johnson, D.: Computers and intractability, A Guide to the theory of NP-compuleteness. W.H.Freeman (1979)

    Google Scholar 

  9. 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 

  10. Moh, T.: A fast public key system with signature and master key functions. Lecture Notes at EE department of Stanford University (May 1999), http://www.usdsi.com/ttm.html

  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. Patarin, J.: Hidden fields 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)

    Chapter  Google Scholar 

  13. Shor, P.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev. 41(2), 303–332 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  14. Tsujii, S., Tadaki, K., Fujioka, R.: Piece in Hand concept for enhanceing the security of multivariate type pulic key cryptosystem: public key without containing all the information of secret key. IACR eprint 2004/366, http://eprint.iacr.org

  15. Wang, Z.: An Improved Medium-Field Equation (MFE) Multivariate Public Key Encryption Scheme. IIH-MISP (2007), http://bit.kuas.edu.tw/iihmsp07/acceptedlistgeneralsession.html

  16. Wang, L.-C., Yang, B.-Y., Hu, Y.-H., Lai, F.: A “Medium-Field” Multivariate Public-Key Encryption Scheme. In: Pointcheval, D. (ed.) CT-RSA 2006. LNCS, vol. 3860, pp. 132–149. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  17. Wang, H., Zhang, H., Wang, Z., Tang, M.: Extended multivariate public key cryptosystems with secure encryption function. SCIENCE CHINA Information Sciences 54(6), 1161–1171 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  18. 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 

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Author information

Authors and Affiliations

  1. School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Xuyun Nie & Zhaohu Xu

  2. Department of Computer Science, Technische Universität Darmstadt, Hochschulstraße 10, 64289, Darmstadt, Germany

    Xuyun Nie & Johannes Buchmann

  3. Network and Data Security Key Laboratory of Sichuan Province, China

    Xuyun Nie & Zhaohu Xu

  4. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, China

    Xuyun Nie

Authors
  1. Xuyun Nie
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  2. Zhaohu Xu
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  3. Johannes Buchmann
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Editor information

Editors and Affiliations

  1. XLIM Laboratory, Department DMI, Université de Limoges, 123, Avenue Albert Thomas, 87000, Limoges, France

    Philippe Gaborit

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Nie, X., Xu, Z., Buchmann, J. (2013). Cryptanalysis of Hash-Based Tamed Transformation and Minus Signature Scheme. In: Gaborit, P. (eds) Post-Quantum Cryptography. PQCrypto 2013. Lecture Notes in Computer Science, vol 7932. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38616-9_10

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  • DOI: https://doi.org/10.1007/978-3-642-38616-9_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38615-2

  • Online ISBN: 978-3-642-38616-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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