Abstract
Multivariate cryptography is one of the main candidates to guarantee the security of communication in the post-quantum era. While multivariate signature schemes are fast and require only modest computational resources, the key sizes of such schemes are quite large. In [14] Petzoldt et al. proposed a way to reduce the public key size of certain multivariate signature schemes like UOV and Rainbow by a large factor. In this paper we show that by using this idea it is possible to speed up the verification process of these schemes, too. For example, we are able to speed up the verification process of UOV by a factor of 5.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bernstein, D.J., Buchmann, J., Dahmen, E. (eds.): Post Quantum Cryptography. Springer, Heidelberg (2009)
Bogdanov, A., Eisenbarth, T., Rupp, A., Wolf, C.: Time-area optimized public-key engines: \(\mathcal{MQ}\)-cryptosystems as replacement for elliptic curves? In: Oswald, E., Rohatgi, P. (eds.) CHES 2008. LNCS, vol. 5154, pp. 45–61. Springer, Heidelberg (2008)
Chen, A.I.-T., Chen, M.-S., Chen, T.-R., Cheng, C.-M., Ding, J., Kuo, E.L.-H., Lee, F.Y.-S., Yang, B.-Y.: SSE implementation of multivariate PKCs on modern x86 CPUs. In: Clavier, C., Gaj, K. (eds.) CHES 2009. LNCS, vol. 5747, pp. 33–48. Springer, Heidelberg (2009)
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)
Ding, J., Yang, B.-Y., Chen, C.-H.O., Chen, M.-S., Cheng, C.M.: New Differential-Algebraic Attacks and Reparametrization of Rainbow. In: Bellovin, S.M., Gennaro, R., Keromytis, A.D., Yung, M. (eds.) ACNS 2008. LNCS, vol. 5037, pp. 242–257. Springer, Heidelberg (2008)
Ding, J., Wolf, C., Yang, B.-Y.: ℓ-Invertible Cycles for \(\mathcal{M}\)ultivariate \(\mathcal{Q}\)uadratic (\(\mathcal{MQ}\)) Public Key Cryptography. In: Okamoto, T., Wang, X. (eds.) PKC 2007. LNCS, vol. 4450, pp. 266–281. Springer, Heidelberg (2007)
Faugère, J.C.: A new efficient algorithm for computing Groebner bases (F4). Journal of Pure and Applied Algebra 139, 61–88 (1999)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman and Company (1979)
Kipnis, A., Patarin, J., Goubin, L.: Unbalanced Oil and Vinegar Signature Schemes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 206–222. Springer, Heidelberg (1999)
Kipnis, A., Shamir, A.: Cryptanalysis of the Oil & Vinegar Signature Scheme. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 257–266. Springer, Heidelberg (1998)
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)
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)
Patarin, J.: The oil and vinegar signature scheme. Presented at the Dagstuhl Workshop on Cryptography (September 1997)
Petzoldt, A., Bulygin, S., Buchmann, J.: A Multivariate Signature Scheme with a partially cyclic public key. In: Proceedings of SCC 2010, pp. 229–235 (2010)
Petzoldt, A., Bulygin, S., Buchmann, J.: Selecting Parameters for the Rainbow Signature Scheme. In: Sendrier, N. (ed.) PQCrypto 2010. LNCS, vol. 6061, pp. 218–240. Springer, Heidelberg (2010)
Petzoldt, A., Bulygin, S., Buchmann, J.: CyclicRainbow – A Multivariate Signature Scheme with a Partially Cyclic Public Key. In: Gong, G., Gupta, K.C. (eds.) INDOCRYPT 2010. LNCS, vol. 6498, pp. 33–48. Springer, Heidelberg (2010)
Petzoldt, A., Bulygin, S., Buchmann, J.: Linear Recurring Sequences for the UOV Key Generation. In: Catalano, D., Fazio, N., Gennaro, R., Nicolosi, A. (eds.) PKC 2011. LNCS, vol. 6571, pp. 335–350. Springer, Heidelberg (2011)
Shor, P.: Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer. SIAM J. Comput. 26(5), 1484–1509
Thomae, E., Wolf, C.: Solving Underdetermined Systems of Multivariate Quadratic Equations Revisited. In: Fischlin, M., Buchmann, J., Manulis, M. (eds.) PKC 2012. LNCS, vol. 7293, pp. 156–171. Springer, Heidelberg (2012)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Petzoldt, A., Bulygin, S., Buchmann, J. (2013). Fast Verification for Improved Versions of the UOV and Rainbow Signature Schemes. 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_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-38616-9_13
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)