New description of SMS4 by an embedding over GF(28)

  • Authors:
  • Wen Ji;Lei Hu

  • Affiliations:
  • State Key Laboratory of Information Security, Graduate School of Chinese Academy of Sciences, Beijing, China;State Key Laboratory of Information Security, Graduate School of Chinese Academy of Sciences, Beijing, China

  • Venue:
  • INDOCRYPT'07 Proceedings of the cryptology 8th international conference on Progress in cryptology
  • Year:
  • 2007

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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.