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A New Construction of Multivariate Public Key Encryption Scheme through Internally Perturbed Plus | SpringerLink
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A New Construction of Multivariate Public Key Encryption Scheme through Internally Perturbed Plus

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Computational Science and Its Applications – ICCSA 2008 (ICCSA 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5073))

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Abstract

Public key cryptography is an important tool in our modern information society. Multivariate public key cryptosystem (MPKC) is a type of public key cryptosystem with high efficiency. In this paper, firstly, we propose a basic multivariate public key encryption scheme which is efficient but insecure. Secondly, we use the internally perturbed plus modifier to modify the basic scheme, and get a improved scheme which is secure against known types of attacks. Finally, we provide a practical implementation of the improved scheme.

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References

  1. Shor, P.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Journal on Computing 26(5), 1484–1509 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  2. 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 

  3. Patarin, J.: Cryptanalysis of the Matsumoto and Imai public key scheme of Eurocrypt 1988. In: Coppersmith, D. (ed.) CRYPTO 1995. LNCS, vol. 963, pp. 248–261. Springer, Heidelberg (1995)

    Google Scholar 

  4. Patarin, J.: Hidden field equations (HFE) and isomorphism of polynomials (IP): Two new families of asymmetric algoritms. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 33–48. Springer, Heidelberg (1996)

    Google Scholar 

  5. Kipnis, A., Shamir, A.: Cryptanalysis of the HFE public key cryptosystem by relinearization. In: Wiener, M.J. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 19–30. Springer, Heidelberg (1999)

    Google Scholar 

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

    Chapter  Google Scholar 

  7. Faugere, J., Joux, A.: Algebraic cryptoanalysis Hidden Field Equation (HFE) cryptosystems using Grober bases. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 44–60. Springer, Heidelberg (2003)

    Google Scholar 

  8. Moh, T.: A fast public key system with signature and master key functions. Lecure notes at EE department of standford university (1999)

    Google Scholar 

  9. Wang, L., Chang, F.: Tractable rational map cryptosystems (revised on December 28, 2006), http://eprint.iacr.org/2004/046

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

    Chapter  Google Scholar 

  11. 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 

  12. Ding, J., Schmidt, D.: The new TTM implementation is not secure. In: Proceeding of Inernational Workshop on Coding, Cryptography and Combinatorics (CCC 2003), pp. 106–121 (2003)

    Google Scholar 

  13. Nie, X., Hu, L., Li, J., Updegrove, C., Ding, J.: Breaking a new instance of TTM cryptosystem. In: Zhou, J., Yung, M., Bao, F. (eds.) ACNS 2006. LNCS, vol. 3989, pp. 210–225. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  14. Joux, A., Kunz-Jaquces, S., Muller, F., Ricordel, P.-M.: Cryptanalysis of the tractable rational map cryptosystem. In: Vaudenay, S. (ed.) PKC 2005. LNCS, vol. 3386, pp. 258–274. Springer, Heidelberg (2005)

    Google Scholar 

  15. 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 

  16. Yang, B., Chen, J.: 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)

    Google Scholar 

  17. Coppersmith, D., Stern, J., Vaudeny, S.: The security of the birational permutation signature scheme. J. Cryptology 10(3), 207–221 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  18. Ars, G., Faugere, J., Imai, H., Kawazoe, M., Sugita, M.: Comparision between XL and Grobner bases algorithms. In: Lee, P.J. (ed.) ASIACRYPT 2004. LNCS, vol. 3329, pp. 338–353. Springer, Heidelberg (2004)

    Google Scholar 

  19. 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 

  20. Yang, B., Chen, J., Courtois, N.: On asymptotic security estimats in XL and Grobner bases related algebraic cryptanalysis. In: López, J., Qing, S., Okamoto, E. (eds.) ICICS 2004. LNCS, vol. 3269, pp. 401–413. Springer, Heidelberg (2004)

    Google Scholar 

  21. Blake, I., Seroussi, G., Smart, N.: Elliptic curves in cryptography. Cambridge Unversity Press, Cambridge (1999)

    MATH  Google Scholar 

  22. Courtois, N., Goubin, L., Patrin, J.: Sflash: Primitive specification (second revised version), Submissions, Sflash, 11 pages (2002), https://www.cosic.east.kuleuven.be/nessie

  23. Courtois, N., Goubin, L., Patrin, J.: Quartz: Primitive specification (second revised version), Submissions, Quartz, 18 pages (2001), https://www.cosic.east.kuleuven.be/nessie

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

    Google Scholar 

  25. Ding, J., Schmidt, D.: Cryptanalysis of HEFV and the internal perturbation of HFE. In: Vaudenay, S. (ed.) PKC 2005. LNCS, vol. 3386, pp. 288–301. Springer, Heidelberg (2005)

    Google Scholar 

  26. Ding, J., Gower, J.: 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 

  27. Faugere, J.: A new efficient algorithm for computing Grobner bases(F4). Journal of Pure and Applied Algebra 139, 61–88 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  28. Fouque, P.-A., Granboulan, L., Stern, J.: Differential cryptanalysis for multivariate schemes. In: Cramer, R.J.F. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 341–353. Springer, Heidelberg (2005)

    Google Scholar 

  29. Shamir, A.: Efficient signature schemes based on birational permutations. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 257–266. Springer, Heidelberg (1998)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, 100876, P.R.China

    Zhiwei Wang, Shihui Zheng & Yixian Yang

  2. School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, 610054, P.R.china

    Xuyun Nie

  3. Sony (China) Research Laboratory,  , Beijing, 100080, P.R.China

    Zhihui Zhang

Authors
  1. Zhiwei Wang
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  2. Xuyun Nie
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  3. Shihui Zheng
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  4. Yixian Yang
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  5. Zhihui Zhang
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Editor information

Osvaldo Gervasi Beniamino Murgante Antonio Laganà David Taniar Youngsong Mun Marina L. Gavrilova

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© 2008 Springer-Verlag Berlin Heidelberg

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Wang, Z., Nie, X., Zheng, S., Yang, Y., Zhang, Z. (2008). A New Construction of Multivariate Public Key Encryption Scheme through Internally Perturbed Plus. In: Gervasi, O., Murgante, B., Laganà, A., Taniar, D., Mun, Y., Gavrilova, M.L. (eds) Computational Science and Its Applications – ICCSA 2008. ICCSA 2008. Lecture Notes in Computer Science, vol 5073. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69848-7_1

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  • DOI: https://doi.org/10.1007/978-3-540-69848-7_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-69840-1

  • Online ISBN: 978-3-540-69848-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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