Nonlinearity Properties of the Mixing Operations of the Block Cipher IDEA

  • Hamdi Murat Yıldırım
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2904)


In this paper we study the nonlinearity properties of the mixing operations ⊙, \(\boxplus\) and ⊕ used in IDEA. We prove that the nonlinearity of the vector function corresponding to the multiplication operation ⊙ is zero for some key points. The Multiplication-Addition (MA) structure of IDEA is slightly changed to avoid the linearities due to these points and we suggest a new structure called RMA. The nonlinearity of MA, RMA and their composition are compared.


Block Cipher Nonlinearity Property Computational Graph Iterate Round Strict Avalanche Criterion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aras, E., Yücel, M.D.: Performance Evaluation of Safer K-64 and S-boxes of Safer Family. Turkish Journal of Electrical Engineering & Computer Sciences 9(2), 161–175 (2001)Google Scholar
  2. 2.
    Daeman, J., Govaerts, R., Vandewalle, J.: Weak Keys for IDEA. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 224–231. Springer, Heidelberg (1994)Google Scholar
  3. 3.
    Lai, X., Massey, J.L.: A Proposal for a New Block Encryption Standard. In: Damgård, I.B. (ed.) EUROCRYPT 1990. LNCS, vol. 473, pp. 389–404. Springer, Heidelberg (1991)Google Scholar
  4. 4.
    Lai, X.: On the design and security of block cipher. ETH Series in Informaion Processing, vol. 1. Hartung-Gorre Verlag, Konstanz (1992)Google Scholar
  5. 5.
    Lai, X., Massey, J.L., Murphy, S.: Markov Cipher and Differential Cryptanalysis. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 17–38. Springer, Heidelberg (1991)Google Scholar
  6. 6.
    Nyberg, K.: On the construction of highly nonlinear permutations. In: Rueppel, R.A. (ed.) EUROCRYPTO 1992. LNCS, vol. 658, pp. 89–94. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  7. 7.
    Measuring Boolean Function Nonlinearity by Walsh Transform,
  8. 8.
    Webster, A.F., Tavares, S.E.: On the design of S-Boxes. In: Williams, H.C. (ed.) CRYPTO 1985. LNCS, vol. 218, pp. 523–534. Springer, Heidelberg (1986)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Hamdi Murat Yıldırım
    • 1
  1. 1.Department of MathematicsMiddle East Technical UniversityAnkaraTurkey

Personalised recommendations