Abstract
In this paper, we study single-cycle T-functions which have important applications in new cryptographic algorithms. We present the algebraic normal form (ANF) of all single-cycle T-functions and the enumeration of single-cycle functions, which reveal many mysterious aspects of such functions. We also investigate the linear complexity and the k-error complexity of single-cycle T-functions when n=2t, the results also reflect the good stability of single-cycle T-functions.
This work was supported by National Natural Science Foundation of China (90304007) and China Postdoctoral Science Foundation.
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Benony, V., Recher, F., Wegrzynowski, E., Fontaine, C.: An Improved Method to Retrieve Internal State of Klimov-Shamir Pseudo-Random Sequence Generators. In: Helleseth, T., Sarwate, D., Song, H.-Y., Yang, K. (eds.) SETA 2004. LNCS, vol. 3486, pp. 138–142. Springer, Heidelberg (2005)
Ding, C., Xiao, G., Shan, W.: The Stability Theory of Stream Ciphers. Springer, Heidelberg (1991)
Games, R.A., Chan, A.H.: A Fast Algorithm for Determining the Complexity of a Binary Sequence with Period 2n. IEEE Transactions on Information Theory 29(1), 144–146 (1983)
Hong, J., Lee, D.H., Yeom, Y., Han, D.: A New Class of Single Cycle T-functions. In: Gilbert, H., Handschuh, H. (eds.) FSE 2005. LNCS, vol. 3557, pp. 68–82. Springer, Heidelberg (2005)
Klimov, A., Shamir, A.: A New Class of Invertible Mappings. In: Kaliski Jr., B.S., Koç, Ç.K., Paar, C. (eds.) CHES 2002. LNCS, vol. 2523, pp. 470–483. Springer, Heidelberg (2003)
Klimov, A., Shamir, A.: Cryptographic Applications of T-Functions. In: Matsui, M., Zuccherato, R.J. (eds.) SAC 2003. LNCS, vol. 3006, pp. 248–261. Springer, Heidelberg (2004)
Klimov, A.B., Shamir, A.: New Cryptographic Primitives Based on Multiword T-Functions. In: Roy, B., Meier, W. (eds.) FSE 2004. LNCS, vol. 3017, pp. 1–15. Springer, Heidelberg (2004)
Kurosawa, K., Sato, F., Sakata, T., Kishmoto, W.: A Relationship Between Linear Complexity and k-error Linear Complexity. IEEE Transactions on Information Theory 46(2), 694–698 (2000)
Massey, J.L.: Shift-register syuthesis and BCH decoding. IEEE Transactions on Information Theory 15, 122–127 (1969)
Meidl, W.: On the Stability of 2n Periodic Binary Sequences. IEEE Transactions on Information Theory 51(3), 1151–1155 (2005)
Molland, H., Helleseth, T.: A linear weakness in the Klimov-Shamir T-function. In: Proceedings of the 2005 IEEE Int. Symposium on Information Theory, pp. 1106–1110 (2005)
Stamp, M., Martin, C.F.: An Algorithm for the k-error Linear Complexity of Binary Sequences with Period 2n. IEEE Transactions on Information Theory 39(4), 1398–1401 (1993)
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Zhang, W., Wu, CK. (2006). The Algebraic Normal Form, Linear Complexity and k-Error Linear Complexity of Single-Cycle T-Function. In: Gong, G., Helleseth, T., Song, HY., Yang, K. (eds) Sequences and Their Applications – SETA 2006. SETA 2006. Lecture Notes in Computer Science, vol 4086. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11863854_34
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DOI: https://doi.org/10.1007/11863854_34
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44523-4
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