A Five-Round Algebraic Property of the Advanced Encryption Standard

  • Jianyong Huang
  • Jennifer Seberry
  • Willy Susilo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5222)


This paper presents a five-round algebraic property of the Advanced Encryption Standard (AES). In the proposed property, we modify twenty bytes from five intermediate values at some fixed locations in five consecutive rounds, and we show that after five rounds of operations, such modifications do not change the intermediate result and finally still produce the same ciphertext. We introduce an algorithm named δ, and the algorithm accepts a plaintext and a key as two inputs and outputs twenty bytes, which are used in the five-round property. We demonstrate that the δ algorithm has 20 variants for AES-128, 28 variants for AES-192 and 36 variants for AES-256. By employing the δ algorithm, we define a modified version of the AES algorithm, the δAES. The δAES calls the δ algorithm to generate twenty bytes, and uses these twenty bytes to modify the AES round keys. The δAES employs the same key scheduling algorithm, constants and round function as the AES. For a plaintext and a key, the AES and the δAES produce the same ciphertext.


AES A Five-Round Algebraic Property of the AES Algorithm δ Variants of Algorithm δ Linear Equations δAES 


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  1. 1.
    Daemen, J., Rijmen, V.: AES Proposal: Rijndael, AES Round 1 Technical Evaluation CD-1: Documentation, National Institute of Standards and Technology (1998)Google Scholar
  2. 2.
    Biham, E., Shamir, A.: Differential Cryptanalysis of the Data Encryption Standard. Springer, Heidelberg (1993)Google Scholar
  3. 3.
    Matsui, M.: Linear Cryptoanalysis Method for DES Cipher. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 386–397. Springer, Heidelberg (1994)Google Scholar
  4. 4.
    NIST: Federal Information Processing Standards (FIPS) 197: Advanced Encryption Standard (AES). National Institute of Standards and Technology (November 26, 2001)Google Scholar
  5. 5.
    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)CrossRefGoogle Scholar
  6. 6.
    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)CrossRefGoogle Scholar
  7. 7.
    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
  8. 8.
    Barkan, E., Biham, E.: In How Many Ways Can You Write Rijndael? In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 160–175. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  9. 9.
    Gilbert, H., Minier, M.: A Collision Attack on 7 Rounds of Rijndael. In: The Third Advanced Encryption Standard Candidate Conference, pp. 230–241 (2000)Google Scholar
  10. 10.
    Daemen, J., Knudsen, L., Rijmen, V.: The Block Cipher Square. In: Biham, E. (ed.) FSE 1997. LNCS, vol. 1267, pp. 149–165. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  11. 11.
    Ferguson, N., Kelsey, J., Lucks, S., Schneier, B., Stay, M., Wagner, D., Whiting, D.: Improved Cryptanalysis of Rijndael. In: Schneier, B. (ed.) FSE 2000. LNCS, vol. 1978, pp. 213–230. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  12. 12.
    Lucks, S.: Attacking Seven Rounds of Rijndael under 192-bit and 256-bit Keys. In: The Third Advanced Encryption Standard Candidate Conference, pp. 215–229 (2000)Google Scholar
  13. 13.
    Akkar, M.L., Giraud, C.: An Implementation of DES and AES, Secure against Some Attacks. In: Koç, Ç.K., Naccache, D., Paar, C. (eds.) CHES 2001. LNCS, vol. 2162, pp. 309–318. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  14. 14.
    Golic, J., Tymen, C.: Multiplicative Masking and Power Analysis of AES. In: Kaliski Jr., B.S., Koç, Ç.K., Paar, C. (eds.) CHES 2002. LNCS, vol. 2523, pp. 198–212. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  15. 15.
    Biryukov, A.: The Design of a Stream Cipher LEX. In: Biham, E., Youssef, A.M. (eds.) SAC 2006. LNCS, vol. 4356, pp. 67–75. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  16. 16.
    Daemen, J., Rijmen, V.: A New MAC Construction ALRED and a Specific Instance ALPHA-MAC. In: Gilbert, H., Handschuh, H. (eds.) FSE 2005. LNCS, vol. 3557, pp. 1–17. Springer, Heidelberg (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Jianyong Huang
    • 1
  • Jennifer Seberry
    • 1
  • Willy Susilo
    • 1
  1. 1.Centre for Computer and Information Security Research (CCISR) School of Computer Science and Software EngineeringUniversity of WollongongAustralia

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