Abstract
A New digital signature scheme based on Stepwise Triangular Scheme (STS) is proposed. The proposed trapdoor has resolved the vulnerability of STS and secure against both Gröbner Bases and Rank Attacks. In addition, as a basic trapdoor, it is more efficient than the existing systems. With the efficient implementation, the Multivariate Public Key Cryptosystems (MPKC) signature public key has the signature longer than the message by less than 25 %, for example.
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Baena, J., Clough, C., Ding, J.: Square-Vinegar signature scheme. In: Buchmann, J., Ding, J. (eds.) PQCrypto 2008. LNCS, vol. 5299, pp. 17–30. Springer, Heidelberg (2008)
Braeken, A., Wolf, C., Preneel, B.: A study of the security of unbalanced oil and vinegar signature schemes. In: Menezes, A. (ed.) CT-RSA 2005. LNCS, vol. 3376, pp. 29–43. Springer, Heidelberg (2005)
Chen, J.M., Yang, B.Y.: A more secure and efficacious TTS signature scheme. In: Lim, J.-I., Lee, D.-H. (eds.) ICISC 2003. LNCS, vol. 2971, pp. 320–338. Springer, Heidelberg (2004)
Clough, C., Baena, J., Ding, J., Yang, B.Y., Chen, M.S.: Square, a new multivariate encryption scheme. In: Fischlin, M. (ed.) CT-RSA 2009. LNCS, vol. 5473, pp. 252–264. Springer, Heidelberg (2009)
Coppersmith, D., Stern, J., Vaudenay, S.: Attacks on the birational permutation signature schemes. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 435–443. Springer, Heidelberg (1994)
Courtois, N., Daum, M., Felke, P.: On the security of HFE, HFEv- and Quartz. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 337–350. Springer, Heidelberg (2003)
Courtois, N., Goubin, L., Patarin, J.: SFLASHv3, a fast asymmetric signature scheme. Cryptology ePrint Archive, Report 2003/211 (October 2003), http://eprint.iacr.org/2003/211
Ding, J.: A new variant of the Matsumoto-Imai cryptosystem through perturbation. In: Bao, F., Deng, R., Zhou, J. (eds.) PKC 2004. LNCS, vol. 2947, pp. 305–318. Springer, Heidelberg (2004)
Ding, J., Schmidt, D.: Cryptanalysis of HFEv and internal perturbation of HFE. In: Vaudenay, S. (ed.) PKC 2005. LNCS, vol. 3386, pp. 288–301. Springer, Heidelberg (2005)
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., 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)
Ding, J., Wagner, J.: Cryptanalysis of rational multivariate public key cryptosystems. In: Buchmann, J., Ding, J. (eds.) PQCrypto 2008. LNCS, vol. 5299, pp. 124–136. Springer, Heidelberg (2008)
Dubois, V., Granboulan, L., Stern, J.: Cryptanalysis of HFE with internal perturbation. In: Okamoto, T., Wang, X. (eds.) PKC 2007. LNCS, vol. 4450, pp. 249–265. Springer, Heidelberg (2007)
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)
Faugère, J.C., Joux, A.: Algebraic cryptanalysis of hidden field equation (HFE) cryptosystems using Gröbner bases. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 44–60. Springer, Heidelberg (2003)
Fouque, P.A., Granboulan, L., Stern, J.: Differential cryptanalysis for multivariate schemes. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 341–353. Springer, Heidelberg (2005)
Goubin, L., Courtois, N.: Cryptanalysis of the TTM cryptosystem. In: Okamoto, T. (ed.) ASIACRYPT 2000. LNCS, vol. 1976, pp. 44–57. Springer, Heidelberg (2000)
Hasegawa, S., Kaneko, T.: An attacking method for a public-key cryptosystem based on the difficulty of solving a system of non-linear equations. In: Proc. 10th SITA, JA5-3 (November 1987) (in Japanese)
Hashimoto, Y., Sakurai, K.: On construction of signature schemes based on birational permutations over noncommutative rings. In: Proceedings of the First International Conference on Symbolic Computation and Cryptography (SCC 2008), pp. 218–227 (2008)
Kasahara, M., Sakai, R.: A construction of public key cryptosystem for realizing ciphertext of size 100 bit and digital signature scheme. IEICE Transactions on Fundamentals E87-A(1) , 102–109 (2004)
Kasahara, M., Sakai, R.: A construction of public-key cryptosystem based on singular simultaneous equations. IEICE Transactions on Fundamentals E88-A(1), 74–80 (2005)
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)
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)
Matsumoto, T., Imai, H., Harashima, H., Miyakawa, H.: A class of asymmetric cryptosystems using obscure representations of enciphering functions. In: 1983 National Convention Record on Information Systems, IECE Japan, S8-5 (1983) (in Japanese)
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)
Moh, T.T.: A public key system with signature and master key functions. Communications in Algebra 27(5), 2207–2222 (1999)
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)
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) (transparencies)
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)
Patarin, J., Courtois, N., Goubin, L.: QUARTZ, 128-bit long digital signatures. In: Naccache, D. (ed.) CT-RSA 2001. LNCS, vol. 2020, pp. 282–297. Springer, Heidelberg (2001)
Shamir, A.: Efficient signature schemes based on birational permutations. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 1–12. Springer, Heidelberg (1994)
Tsujii, S.: Public key cryptosystem using nonlinear equations. In: Proc. 8th SITA, December 1985, pp. 156–157 (1985) (in Japanese)
Tsujii, S., Kurosawa, K., Itoh, T., Fujioka, A., Matsumoto, T.: A public-key cryptosystem based on the difficulty of solving a system of non-linear equations. IEICE Transactions (D), J69-D(12) (1986) (1963–1970) (in Japanese)
Tsujii, S., Fujioka, A., Hirayama, Y.: Generalization of the public-key cryptosystem based on the difficulty of solving a system of non-linear equations. IEICE Transactions (A), J72-A(2), 390–397 (1989) (in Japanese); An English translation of [35] is included in [36] as an appendix
Tsujii, S., Tadaki, K., Fujita, R.: Piece in hand concept for enhancing the security of multivariate type public key cryptosystems: public key without containing all the information of secret key. Cryptology ePrint Archive, Report 2004/366 (December 2004), http://eprint.iacr.org/2004/366
Tsujii, S., Tadaki, K., Gotaishi, M., Fujita, R., Kasahara, M.: Proposal of PPS multivariate public key cryptosystems. Cryptology ePrint Archive, Report 2009/264 (June 2009), http://eprint.iacr.org/2009/264
Tsujii, S., Tadaki, K., Gotaishi, M., Fujita, R., Kasahara, M.: Proposal of integrated MPKC: PPS — STS enhanced by perturbed piece in hand method —. Technical Report of IEICE, ISEC2009-27, SITE2009-19, ICSS2009-41 (2009-2007) (July 2009) (in Japanese)
Wang, L.C., Chang, F.H.: Revision of tractable rational map cryptosystem. Cryptology ePrint Archive, Report 2004/046 (2006), http://eprint.iacr.org/2004/046
Wang, L.C., Hu, Y.H., Lai, F., Chou, C.Y., Yang, B.Y.: Tractable rational map signature. In: Vaudenay, S. (ed.) PKC 2005. LNCS, vol. 3386, pp. 244–257. Springer, Heidelberg (2005)
Wang, L.C., Yang, B.Y., Hu, Y.H., Lai, F.: A “medium-field” multivariate public-key encryption scheme. In: Pointcheval, D. (ed.) CT-RSA 2006. LNCS, vol. 3860, pp. 132–149. Springer, Heidelberg (2006)
Wolf, C., Braeken, A., Preneel, B.: Efficient cryptanalysis of RSE(2)PKC and RSSE(2)PKC. In: Blundo, C., Cimato, S. (eds.) SCN 2004. LNCS, vol. 3352, pp. 294–309. Springer, Heidelberg (2005)
Yang, B.Y., Chen, J.M.: Building secure tame-like multivariate public-key cryptosystems: the new TTS. In: Boyd, C., González Nieto, J.M. (eds.) ACISP 2005. LNCS, vol. 3574, pp. 518–531. Springer, Heidelberg (2005)
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Tsujii, S., Gotaishi, M., Tadaki, K., Fujita, R. (2010). Proposal of a Signature Scheme Based on STS Trapdoor. 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_15
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