On Some Weak Extensions of AES and BES

  • Jean Monnerat
  • Serge Vaudenay
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3269)


In 2002, Murphy and Robshaw introduced an extension BES of AES and argued this could compromise the security of AES. We introduce here two block-ciphers CES and Big-BES that are some extensions of the AES and BES respectively in the spirit of Hensel lifting extensions. They are defined similarly to the AES respectively BES except that every operations are performed in a ring structure including the field GF(28). We show that the AES and BES can be embedded in their extensions. More precisely, by restricting these extensions on a given subset, we obtain a fully equivalent description of the AES and BES. Furthermore, we show that these natural extensions are trivially weak by describing a cryptanalysis of them despite it leads to no consequence about the security of AES or BES. This shows that (except the nice mathematical construction) the Murphy-Robshaw extension might be pointless.


AES BES Rijndael 


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  1. 1.
    Aoki, K., Vaudenay, S.: On the Use of GF-Inversion as a Cryptographic Primitive. Selected Areas in Cryptography (2003)Google Scholar
  2. 2.
    Barkan, E., Biham, E.: How Many Ways Can You Write Rijndael? In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 160–175. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  3. 3.
    Biham, E., Shamir, A.: Differential Cryptanalysis of the Data Encryption Standard. Springer, New York (1993)zbMATHGoogle Scholar
  4. 4.
    Catalano, D., Nguyen, P.Q., Stern, J.: The Hardness of Hensel Lifting: The Case of RSA and Discrete Logarithm. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 299–310. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  5. 5.
    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)CrossRefGoogle Scholar
  6. 6.
    Daemen, J., Rijmen, V.: The Design of Rijndael: AES-The Advanced Encryption Standard. Springer, Heidelberg (2002)zbMATHGoogle Scholar
  7. 7.
    Ferguson, N., Shroeppel, R., Whiting, D.: A Simple Algebraic Representation of Rijndael. In: Vaudenay, S., Youssef, A.M. (eds.) SAC 2001. LNCS, vol. 2259, pp. 103–111. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  8. 8.
    Lidl, R., Niederreiter, H.: Finite Fields. Encyclopedia of Mathematics and its Applications, vol. 20. Cambridge University Press, Cambridge (1997)Google Scholar
  9. 9.
    Matsui, M.: Linear Cryptanalysis method for DES Cipher. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 386–397. Springer, Heidelberg (1994)Google Scholar
  10. 10.
    Murphy, S., Robshaw, M.J.B.: New Observations on Rijndael, NISTAES website (August 2000)Google Scholar
  11. 11.
    Murphy, S., Robshaw, M.J.B.: Essential Algebraic Structure Within the AES. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 1–16. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  12. 12.
    National Institute of Standards and Technology, Advanced Encryption Standard, FIPS 197 (November 26, 2001)Google Scholar
  13. 13.
    Okamoto, T., Uchiyama, S.: A New Public-Key Cryptosystem as Secure as Factoring. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 308–318. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  14. 14.
    Satoh, T., Araki, K.: Fermat Quotients and the Polynomial Time Discrete Log Algorithm for Anomalous Elliptic Curves. Commentarii Math. Univ. St. Pauli 47, 81–92 (1998)zbMATHMathSciNetGoogle Scholar
  15. 15.
    Smart, N.P.: The Discrete Logarithm Problem on Elliptic Curves of Trace One. Journal of Cryptology 12, 193–196 (1999)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Jean Monnerat
    • 1
  • Serge Vaudenay
    • 1
  1. 1.EPFLSwitzerland

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