EFLASH: A New Multivariate Encryption Scheme

  • Ryann CartorEmail author
  • Daniel Smith-Tone
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11349)


Multivariate Public Key Cryptography is a leading option for security in a post quantum society. In this paper we propose a new encryption scheme, EFLASH, and analyze its efficiency and security.


Multivariate cryptography HFE PFLASH Discrete differential MinRank 


  1. 1.
    Tao, C., Diene, A., Tang, S., Ding, J.: Simple matrix scheme for encryption. In: Gaborit, P. (ed.) PQCrypto 2013. LNCS, vol. 7932, pp. 231–242. Springer, Heidelberg (2013). Scholar
  2. 2.
    Porras, J., Baena, J., Ding, J.: ZHFE, a new multivariate public key encryption scheme. [30], pp. 229–245 (2014)Google Scholar
  3. 3.
    Yasuda, T., Sakurai, K.: A multivariate encryption scheme with rainbow. In: Qing, S., Okamoto, E., Kim, K., Liu, D. (eds.) ICICS 2015. LNCS, vol. 9543, pp. 236–251. Springer, Cham (2016). Scholar
  4. 4.
    Moody, D., Perlner, R., Smith-Tone, D.: An asymptotically optimal structural attack on the ABC multivariate encryption scheme. [30], pp. 180–196 (2014)Google Scholar
  5. 5.
    Moody, D., Perlner, R., Smith-Tone, D.: Key recovery attack on the cubic ABC simple matrix multivariate encryption scheme. In: Avanzi, R., Heys, H. (eds.) SAC 2016. LNCS, vol. 10532, pp. 543–558. Springer, Cham (2017). Scholar
  6. 6.
    Moody, D., Perlner, R., Smith-Tone, D.: Improved attacks for characteristic-2 parameters of the cubic ABC simple matrix encryption scheme. [29], pp. 255–271 (2017)Google Scholar
  7. 7.
    Cabarcas, D., Smith-Tone, D., Verbel, J.A.: Key recovery attack for ZHFE. [29], pp. 289–308 (2017)CrossRefGoogle Scholar
  8. 8.
    Perlner, R., Petzoldt, A., Smith-Tone, D.: Total break of the SRP encryption scheme. In: Adams, C., Camenisch, J. (eds.) SAC 2017. LNCS, vol. 10719, pp. 355–373. Springer, Cham (2018). Scholar
  9. 9.
    Matsumoto, T., Imai, H.: Public quadratic polynomial-tuples for efficient signature-verification and message-encryption. In: Barstow, D., et al. (eds.) EUROCRYPT 1988. LNCS, vol. 330, pp. 419–453. Springer, Heidelberg (1988). Scholar
  10. 10.
    Ding, J., Dubois, V., Yang, B.-Y., Chen, O.C.-H., 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. LNCS, vol. 5126, pp. 691–701. Springer, Heidelberg (2008). Scholar
  11. 11.
    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). Scholar
  12. 12.
    Cartor, R., Smith-Tone, D.: An updated security analysis of PFLASH. [29], pp. 241–254 (2017)CrossRefGoogle Scholar
  13. 13.
    Patarin, J., Goubin, L., Courtois, N.: Improved algorithms for isomorphisms of polynomials. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 184–200. Springer, Heidelberg (1998). Scholar
  14. 14.
    Patarin, J.: Hidden fields equations (HFE) and isomorphisms of polynomials (IP): two new families of asymmetric algorithms. In: Maurer, U. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 33–48. Springer, Heidelberg (1996). Scholar
  15. 15.
    Berlekamp, E.R.: Factoring polynomials over large finite fields. Math. Comput. 24, 713–735 (1970)MathSciNetCrossRefGoogle Scholar
  16. 16.
    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). Scholar
  17. 17.
    Bettale, L., Faugère, J., Perret, L.: Cryptanalysis of HFE, multi-HFE and variants for odd and even characteristic. Des. Codes Cryptogr. 69, 1–52 (2013)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Daniels, T., Smith-Tone, D.: Differential properties of the HFE cryptosystem. [30], pp. 59–75 (2014)Google Scholar
  19. 19.
    Chen, M.S., Yang, B.Y., Smith-Tone, D.: PFLASH - secure asymmetric signatures on smart cards. In: Lightweight Cryptography Workshop 2015 (2015).
  20. 20.
    Hashimoto, Y.: Cryptanalysis of multi-HFE. IACR Cryptol. ePrint Arch. 2015, 1160 (2015)Google Scholar
  21. 21.
    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). Scholar
  22. 22.
    Kipnis, A., Shamir, A.: Cryptanalysis of the oil and vinegar signature scheme. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 257–266. Springer, Heidelberg (1998). Scholar
  23. 23.
    Ding, J., Kleinjung, T.: Degree of regularity for HFE-. IACR Cryptol. ePrint Arch. 2011, 570 (2011)zbMATHGoogle Scholar
  24. 24.
    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). Scholar
  25. 25.
    Vates, J., Smith-Tone, D.: Key recovery attack for all parameters of HFE-. [29], pp. 272–288 (2017)CrossRefGoogle Scholar
  26. 26.
    Bardet, M., Faugere, J.C., Salvy, B.: On the complexity of Gröbner basis computation of semi-regular overdetermined algebraic equations. In: Proceedings of the International Conference on Polynomial System Solving (2004)Google Scholar
  27. 27.
    Bardet, M., Faugére, J., Salvy, B., Yang, B.: Asymptotic behaviour of the degree of regularity of semi-regular polynomial systems. In: Proceedings of MEGA 2005, Eighth International Symposium on Effective Methods in Algebraic Geometry (2005)Google Scholar
  28. 28.
    Smart, N.P., Albrecht, M.R., Orsini, E., Paterson, K.G., Peer, G.: LIMA: a PQC encryption schemeGoogle Scholar
  29. 29.
    Lange, T., Takagi, T. (eds.): PQCrypto 2017. LNCS, vol. 10346. Springer, Cham (2017). Scholar
  30. 30.
    Mosca, M. (ed.): PQCrypto 2014. LNCS, vol. 8772. Springer, Cham (2014). Scholar

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Authors and Affiliations

  1. 1.Department of MathematicsUniversity of LouisvilleLouisvilleUSA
  2. 2.National Institute of Standards and TechnologyGaithersburgUSA

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