Abstract
The proxy signatures are important cryptosystems that are widely adopted in different applications. Most of the proxy signature schemes so far are based on the hardness of integer factoring, discrete logarithm, and/or elliptic curve. However, Shor proved that the emerging quantum computers can solve the problem of prime factorization and discrete logarithm in polynomial-time, which threatens the security of current RSA, ElGamal, ECC, and the proxy signature schemes based on these problems. We propose a novel proxy signature scheme based on the problem of Isomorphism of Polynomials (IP) which belongs to a major category of Multivariate Public Key Cryptography (MPKC). Through security discussion, our scheme can reach the same security level as the signature scheme based on IP problem. The most attractive advantage of our scheme should be its feature to potentially resist the future quantum computing attacks. Our scheme also owns some important properties of proxy signature schemes, such as strong unforgeability, strong identifiability, strong undeniability, secret-key’s dependence, distinguishability, etc. The scheme is implemented in C/C++ programming language, and the performance shows that the scheme is efficient. The parameters we choose can let security level of the scheme up to 286.59.
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References
Awasthi, A., Lal, S.: Proxy Blind Signature Scheme. Transaction on Cryptology 2(1), 5–11 (2005)
Bernstein, D.J., Buchmann, J., Dahmen, E.: Post Quantum Cryptography, Department of Computer Science, University of Illinois, Chicago. Springer, Heidelberg (2009)
Boldyreva, A., Palacio, A., Warinschi, B.: Secure Proxy Signature Schemes for Delegation of Signing Rights. Journal of Cryptology 25(1), 57–115 (2012)
Bouillaguet, C., Faugère, J., Fouque, P., Perret, L.: Differential Algorithms for the Isomorphism of Polynomials Problem (2009) (manuscript), http://eprint.iacr.org/2009/583.pdf
Bulygin, S., Petzoldt, A., Buchmann, J.: Towards Provable Security of the Unbalanced Oil and Vinegar Signature Scheme under Direct Attacks. In: Gong, G., Gupta, K.C. (eds.) INDOCRYPT 2010. LNCS, vol. 6498, pp. 17–32. Springer, Heidelberg (2010)
Dubois, V., Granboulan, L., Stern, J.: An Efficient Provable Distinguisher for HFE. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4052, pp. 156–167. Springer, Heidelberg (2006)
Faugère, J.-C., Perret, L.: Polynomial Equivalence Problems: Algorithmic and Theoretical Aspects. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 30–47. Springer, Heidelberg (2006)
Fuchsbauer, G., Pointcheval, D.: Anonymous Proxy Signatures. In: Ostrovsky, R., De Prisco, R., Visconti, I. (eds.) SCN 2008. LNCS, vol. 5229, pp. 201–217. Springer, Heidelberg (2008)
Garey, M.R., Johnson, D.S.: Computers and Intractability, A Guide to the Theory of NP-completeness. W.H. Freeman (1979)
Geiselmann, W., Meier, W.: An Attack on the Isomorphisms of Polynomials Problem with One Secret. International Journal of Information Security 2, 59–64 (2003)
Kim, S., Park, S., Won, D.: Proxy Signatures, Revisited. In: Information and Communications Security, pp. 223–232. Springer, Heidelberg (1997)
Mambo, M., Usuda, K., Okamoto, E.: Proxy Signatures: Delegation of The Power to Sign Messages. IEICE Transactions on Fundamentals, E79-A(9), 1338-1353 (1996)
Mambo, M., Usuda, K., Okamoto, E.: Proxy Signatures for Delegating Signing Operation. In: Proceedings of the 3rd ACM Conference on Computer and Communications Security, pp. 48-57. ACM (1996)
Patarin, J., Goubin, L., Courtois, N.T.: Improved Algorithms for Isomorphisms of Polynomials. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 184–200. Springer, Heidelberg (1998)
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)
Perret, L.: A Fast Cryptanalysis of the Isomorphism of Polynomials with One Secret Problem. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 354–370. Springer, Heidelberg (2005)
Sakumoto, K., Shirai, T., Hiwatari, H.: On Provable Security of UOV and HFE Signature Schemes against Chosen-Message Attack. In: Yang, B.-Y. (ed.) PQCrypto 2011. LNCS, vol. 7071, pp. 68–82. Springer, Heidelberg (2011)
Shor, P.W.: Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer. SIAM J. Comput. 26(5), 1484–1509 (1997)
Levy-dit-Vehel, F., Perret, L.: Polynomial Equivalence Problems. In: Johansson, T., Maitra, S. (eds.) INDOCRYPT 2003. LNCS, vol. 2904, pp. 235–251. Springer, Heidelberg (2003)
Zhang, K.: Threshold Proxy Signature Schemes. In: Okamoto, E. (ed.) ISW 1997. LNCS, vol. 1396, pp. 282–290. Springer, Heidelberg (1998)
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Tang, S., Xu, L. (2012). Proxy Signature Scheme Based on Isomorphisms of Polynomials. In: Xu, L., Bertino, E., Mu, Y. (eds) Network and System Security. NSS 2012. Lecture Notes in Computer Science, vol 7645. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34601-9_9
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