Abstract
Recently, the C * − signature scheme has been completely broken by Dubois et al. [1,2]. As a consequence, the security of SFLASH and other multivariate public key systems have been impaired. The attacks presented in [1,2] rely on a symmetry of the differential of the encryption mapping. In [3], Ding et al. experimentally justify the use projection as a method of avoiding the new attack, and some theoretical backing to this method is given in [4]. In this paper, we derive some properties of the discrete differential, extend the theoretical justification for the reparation in [3], and establish the exact context in which this attack is applicable.
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References
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)
Dubois, V., Fouque, P.A., Stern, J.: Cryptanalysis of SFLASH with Slightly Modified Parameters. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 264–275. Springer, Heidelberg (2007)
Ding, J., Yang, B.Y., Cheng, C.M., Chen, O., Dubois, V.: Breaking the Symmetry: a Way to Resist the New Differential Attack. Cryptology ePrint Archive, Report 2007/366 (2007), http://eprint.iacr.org/
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)
Patarin, J.: Cryptoanalysis 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)
Wolf, C., Preneel, B.: Taxonomy of Public Key Schemes Based on the Problem of Multivariate Quadratic Equations. Cryptology ePrint Archive, Report 2005/077 (2005), http://eprint.iacr.org/
Matsumoto, T., Imai, H.: Public Quadratic Polynominal-Tuples for Efficient Signature-Verification and Message-Encryption. In: Günther, C.G. (ed.) EUROCRYPT 1988. LNCS, vol. 330, pp. 419–453. Springer, Heidelberg (1988)
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)
Mollin, R.A., Small, C.: On Permutation Polynomials over Finite Fields. Internat. J. Math. and Math. Sci. 10, 535–543 (1987)
Lidl, R., Niederreiter, H.: Introduction to Finite Fields and their Applications. Cambridge University Press, New York (1986)
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. 35–49. Springer, Heidelberg (1998)
Clough, C., Baena, J., Ding, J., Yang, B.Y., Chen, M.S.: Square, a New Multivariate Encryption Scheme. In: Fischlin, M. (ed.) RSA Conference 2009. LNCS, vol. 5473, pp. 252–264. Springer, Heidelberg (2009)
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Smith-Tone, D. (2010). Properties of the Discrete Differential with Cryptographic Applications. 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_1
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DOI: https://doi.org/10.1007/978-3-642-12929-2_1
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