Abstract
SMS4 is a 128-bit block cipher which is used in the WAPI standard in China for protecting wireless transmission data. Due to the nature that the functions deployed in the round transformations of SMS4 operate on two different fields GF(28) and GF(2), it is difficult to analyze this cipher algebraically. In this paper we describe a new block cipher called ESMS4, which uses only algebraic operations over GF(28). The new cipher is an extension of SMS4 in the sense that SMS4 can be embedded into ESMS4 with restricted plaintext space and key spaces. Thus, the SMS4 cipher can be investigated through this embedding over GF(28). Based on this new cipher, we represent the SMS4 cipher with an overdetermined, sparse multivariate quadratic equation system over GF(28). Furthermore, we estimate the computational complexity of the XSL algorithm for solving the equation system and find that the complexity is 277 when solving the whole system of equations.
This is a preview of subscription content, log in via an institution to check access.
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
Beijing Data Security Company, The SMS4 Block Cipher (in Chinese), Beijing (2006), available at http://www.oscca.gov.cn/UpFile/200621016423197990.pdf
Cid, C., Leurent, G.: An Analysis of the XSL Algorithm. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol. 3788, pp. 333–352. Springer, Heidelberg (2005)
Courtois, N., Pieprzyk, J.: Cryptanalysis of Block Ciphers with Overdefined Systems of Equations, Cryptology ePrint Archive, Report, /044, 2002 (2002), available at http://eprint.iacr.org/2002/044
Courtois, N., Pieprzyk, J.: Cryptanalysis of Block Ciphers with Overdefined Systems of Equations. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 267–287. Springer, Heidelberg (2002)
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)
Courtois, N., Patarin, J.: About the XL Algorithm over GF(2). In: Joye, M. (ed.) CT-RSA 2003. LNCS, vol. 2612, pp. 141–157. Springer, Heidelberg (2003)
Daemen, J., Rijmen, V.: AES proposal: The Rijndael block cipher. Springer, Heidelberg (1999)
Kipnis, A., Shamir, A.: Cryptanalysis of the HFE Public Key Cryptosystem by Relinearization. In: Wiener, M.J. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 19–30. Springer, Heidelberg (1999)
Lidl, R., Niederreiter, H.: Introduction to Finite Fields and Their Applications. Cambridge University Press, Cambridge (1984)
Liu, F., Ji, W., Hu, L., Ding, J., Lv, S., Pyshkin, A., Weinmann, R.: Analysis of the SMS4 Block Cipher. In: ACISP 2007. LNCS, vol. 4586, pp. 158–170. Springer, Heidelberg (2007)
Murphy, S., Robshaw, M.: Essential Algebraic Structure within the AES. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 1–16. Springer, Heidelberg (2002)
Lim, C., Khoo, K.: An Analysis of XSL Applied to BES. In: FSE 2007. LNCS, vol. 4593, pp. 242–253. Springer, Heidelberg (2007)
Zhang, L., Wu, W.: Difference Fault Attack on the SMS4 Encryption Algorithm (in Chinese). Chinese Journal of Computers 29(9), 1596–1602 (2006)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ji, W., Hu, L. (2007). New Description of SMS4 by an Embedding overGF(28). In: Srinathan, K., Rangan, C.P., Yung, M. (eds) Progress in Cryptology – INDOCRYPT 2007. INDOCRYPT 2007. Lecture Notes in Computer Science, vol 4859. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77026-8_18
Download citation
DOI: https://doi.org/10.1007/978-3-540-77026-8_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77025-1
Online ISBN: 978-3-540-77026-8
eBook Packages: Computer ScienceComputer Science (R0)