Abstract
This paper continues our research of the so-called matrix power function and its application to cryptography. We consider the simplest case of the improved matrix power asymmetric cypher (MPAC). We show that our protocol is resistant to linear algebra attack, which can be applied to the initial version of MPAC to break it in polynomial time. Our main goal is to present the general idea for the choice of public parameters of MPAC protocol to avoid this attack while also avoiding exhaustive search attack.
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Diffie, W., Hellman, M.: New directions in cryptography. IEEE Trans. Inf. Theory 22(6), 644–654 (1976)
Wagner, N.R., Magyarik, M.R.: A Public-key cryptosystem based on the word problem. In: Blakley, G.R., Chaum, D. (eds.) Advances in Cryptology, CRYPTO 1984. Lecture Notes in Computer Science, vol. 196, pp. 19–36. Springer, Berlin (1985)
Ko, K.H., Lee, S.J., Cheon, J.H., Han, J.W., Kang, J., Park, C.: New public-key cryptosystem using braid groups. In: Bellare, M. (ed.) Advances in Cryptology — CRYPTO 2000, CRYPTO 2000. Lecture Notes in Computer Science, vol. 1880, pp. 166–183. Springer, Berlin (2000)
Anshel, I., Anshel, M., Goldfeld, D.: An algebraic method for public-key cryptography. Math. Res. Lett. 6, 287–292 (1999)
Shpilrain, V., Ushakov, A.: The conjugacy search problem in public key cryptography: unnecessary and insufficient. Appl. Algebra Eng. Commun. Comput. 17(3–4), 285–289 (2006)
Sakalauskas, E., Luksys, K.: Matrix power function and its application to block cipher S-box construction. Int. J. Innovative Comput. Inf. Control 8(4), 2655–2664 (2012)
Sakalauskas, E., Listopadskis, N., Tvarijonas, P.: Key agreement protocol (KAP) based on matrix power function. In: Sixth International Conference on Information Research and Applications – i.Tech 2008, Varna, Bulgaria (2008)
Mihalkovič, A., Sakalauskas, E.: Asymmetric cipher based on MPF and its security parameters evaluation. In: Proceedings of the Lithuanian Mathematical Society, Series A, vol. 53, pp. 72–77 (2012)
Sakalauskas, E., Mihalkovich, A.: Candidate one-way function based on matrix power function with conjugation constraints. In: Proceedings of the Bulgarian Cryptography Days, pp. 29–37 (2012)
Sakalauskas, E., Mihalkovich, A.: New asymmetric cipher of non-commuting cryptography class based on matrix power function. Informatica 25(2), 283–298 (2014)
Liu, J., Zhang, H., Jia, J.: A linear algebra attack on the non-commuting cryptography class based on matrix power function. In: Chen, K., Lin, D., Yung, M. (eds.) Information Security and Cryptology, Inscrypt 2016. Lecture Notes in Computer Science, vol. 10143, pp. 343–354. Springer, Cham (2017)
Gantmakher, F.R.: The theory of matrices, vol. 131. American Mathematical Soc. (2000)
Sakalauskas, E., Mihalkovich, A.: Improved asymmetric cipher based on matrix power function resistant to linear algebra attack. Informatica 28(3), 517–524 (2017)
Jenkov.com Tech and Media Labs. http://tutorials.jenkov.com/java-cryptography/index.html
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Mihalkovich, A., Levinskas, M. (2019). Investigation of Matrix Power Asymmetric Cipher Resistant to Linear Algebra Attack. In: Damaševičius, R., Vasiljevienė, G. (eds) Information and Software Technologies. ICIST 2019. Communications in Computer and Information Science, vol 1078. Springer, Cham. https://doi.org/10.1007/978-3-030-30275-7_16
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DOI: https://doi.org/10.1007/978-3-030-30275-7_16
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