Abstract
Multivariate cryptography plays an important role in post-quantum cryptography. Many signature schemes, such as Rainbow remain secure despite the development of several attempted attack algorithms. However, most multivariate signature schemes use relatively large public keys compared with those of other post-quantum signature schemes. In this paper, we present an approach for constructing a multivariate signature scheme based on matrix multiplication. At the same security level, our proposed signature scheme has smaller public key and signature sizes compared with the Rainbow signature scheme.
Supported by JST CREST Grant Number JPMJCR14D6, Japan.
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References
Beullens, W.: Improved cryptanalysis of UOV and rainbow, Cryptology ePrint Archive, Report 2020/1343 (2020). https://eprint.iacr.org/2020/1343
Buchberger, B.: Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal, Ph.D. thesis, Universität Innsbruck (1965)
Chen, L., et al.: Report on Post-quantum Cryptography, NIST Interagency Report 8105 (2016). https://www.nist.gov/publications/report-post-quantum-cryptography
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., Yung, M. (eds.) ACNS 2008. LNCS, vol. 5037, pp. 242–257. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-68914-0_15
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). https://doi.org/10.1007/3-540-45539-6_27
Ding, J., et al.: Rainbow, NIST PQC Project. https://csrc.nist.gov/projects/post-quantum-cryptography/
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). https://doi.org/10.1007/978-3-540-71677-8_16
Ding, J., Schmidt, D.: Rainbow, a new multivariable polynomial signature scheme. In: Ioannidis, J., Keromytis, A., Yung, M. (eds.) ACNS 2005. LNCS, vol. 3531, pp. 164–175. Springer, Heidelberg (2005). https://doi.org/10.1007/11496137_12
Faugère, J.-C.: A New Efficient Algorithm for Computing Gröbner Bases (F4). J. Pure Appl. Algebra 139(1), 61–88 (1999)
Faugère, J.-C., Din, M., Spaenlehauer, P.-J.: Computing loci of rank defects of linear matrices using Gröbner bases and applications to cryptology. In: ISSAC 2010, pp. 257–264 (2010)
Garey, M., Johnson, D.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman and Company, San Francisco (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). https://doi.org/10.1007/3-540-48910-X_15
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). https://doi.org/10.1007/BFb0055733
Moody, D., Perlner, R., Smith-Tone, D.: An asymptotically optimal structural attack on the ABC multivariate encryption scheme. In: Mosca, M. (ed.) PQCrypto 2014. LNCS, vol. 8772, pp. 180–196. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-11659-4_11
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). https://doi.org/10.1007/3-540-68339-9_4
Shor, P.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26(5), 1484–1509 (1997)
Szepieniec, A., Ding, J., Preneel, B.: Extension field cancellation: a new central trapdoor for multivariate quadratic systems. In: Takagi, T. (ed.) PQCrypto 2016. LNCS, vol. 9606, pp. 182–196. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-29360-8_12
Tao, C., Xiang, H., Petzoldt, A., Ding, J.: Simple matrix - a multivariate public key cryptosystem (MPKC) for encryption. Finite Fields Appl. 35, 352–368 (2015)
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). https://doi.org/10.1007/978-3-642-30057-8_10
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Yin, C., Wang, Y., Takagi, T. (2021). (Short Paper) Simple Matrix Signature Scheme. In: Nakanishi, T., Nojima, R. (eds) Advances in Information and Computer Security. IWSEC 2021. Lecture Notes in Computer Science(), vol 12835. Springer, Cham. https://doi.org/10.1007/978-3-030-85987-9_13
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