Abstract
The bit-search generator (BSG) was proposed in 2004 and can be seen as a variant of the shrinking and self-shrinking generators. It has the advantage that it works at rate 1/3 using only one LFSR and some selection logic. We present various attacks on the BSG based on the fact that the output sequence can be uniquely defined by the differential of the input sequence. By knowing only a small part of the output sequence we can reconstruct the key with complexity O(L 320.5 L). This complexity can be significantly reduced in a data/time tradeoff manner to achieve a complexity of O(L 320.27 L) if we have O(20.27 L) of keystream. We also propose a distinguishing attack that can be very efficient if the feedback polynomial is not carefully chosen.
The work described in this paper has been supported in part by the European Commission through the IST Programme under Contract IST-2002-507932 ECRYPT. The information in this document reflects only the author’s views, is provided as is and no guarantee or warranty is given that the information is fit for any particular purpose. The user thereof uses the information at its sole risk and liability.
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References
Coppersmith, D., Krawczyk, H., Mansour, Y.: The shrinking generator. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 22–39. Springer, Heidelberg (1994)
Coppersmith, D., Winograd, S.: Matrix Multiplication via Arithmetic Progressions. J. Symbolic Computation 9, 251–280 (1990)
Ekdahl, P., Meier, W., Johansson, T.: Predicting the Shrinking Generator with Fixed Connections. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 330–344. Springer, Heidelberg (2003)
Ekdahl, P., Johansson, T., Meier, W.: A Note on the Self-Shrinking Generator. In: Proceedings of International Symposium on Information Theory, p. 166. IEEE, Los Alamitos (2003)
Englund, H., Hell, M., Johansson, T.: Correlation attacks using a new class of weak feedback polynomials. In: Roy, B., Meier, W. (eds.) FSE 2004. LNCS, vol. 3017, pp. 127–142. Springer, Heidelberg (2004)
Golić, J.D.: Computation of Low-Weight Parity Check Polynomials. Electronic Letters 32(21), 1981–1982 (1996)
Golić, J.D.: Correlation analysis of the shrinking generator. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 440–457. Springer, Heidelberg (2001)
Golić, J.D., Menicocci, R.: Edit distance correlation attack on the alternating step generator. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 499–512. Springer, Heidelberg (1997)
Golić, J.D., Menicocci, R.: Edit Probability Correlation Attack on the Alternating Step Generator. In: Ding, C., Helleseth, T., Niederreiter, H. (eds.) Sequences and their Applications–SETA 1998. Discrete Mathematics and Theoretical Computer Science, pp. 213–227. Springer, Heidelberg (1999)
Gouget, A., Sibert, H.: The Bit-Search Generator. In: The State of the Art of Stream Ciphers: Workshop Record, Brugge, Belgium, October 2004, pp. 60–68 (2004)
Günther, C.G.: Alternating step generators controlled by de bruijn sequences. In: Price, W.L., Chaum, D. (eds.) EUROCRYPT 1987. LNCS, vol. 304, pp. 5–14. Springer, Heidelberg (1988)
Johansson, T.: Reduced Complexity Correlation Attacks on Two Clock-Controlled Generators. In: Ohta, K., Pei, D. (eds.) ASIACRYPT 1998. LNCS, vol. 1514, pp. 342–357. Springer, Heidelberg (1998)
Krause, M.: BDD-based cryptanalysis of keystream generators. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 222–237. Springer, Heidelberg (2002)
McEliece, R.J.: Finite Fields for Computer Scientists and Engineers. Kluwer Academic Publishers, Dordrecht (1987)
Meier, W., Staffelbach, O.: Fast correlation attacks on stream ciphers. In: Günther, C.G. (ed.) EUROCRYPT 1988. LNCS, vol. 330, pp. 301–314. Springer, Heidelberg (1988)
Meier, W., Staffelbach, O.: The self-shrinking generator. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 205–214. Springer, Heidelberg (1995)
Mihaljevic, M.: A Faster Cryptanalysis of the Self-Shrinking Generator. In: Pieprzyk, J.P., Seberry, J. (eds.) ACISP 1996. LNCS, vol. 1172, pp. 182–189. Springer, Heidelberg (1996)
Simpson, L., Golić, J.D., Dawson, E.: A probabilistic correlation attack on the shrinking generator. In: Boyd, C., Dawson, E. (eds.) ACISP 1998. LNCS, vol. 1438, pp. 147–158. Springer, Heidelberg (1998)
Strassen, V.: Gaussian Elimination is Not Optimal. Numerische Mathematik 13, 354–356 (1969)
Wagner, D.: A generalized birthday problem. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 288–303. Springer, Heidelberg (2002)
Zenner, E., Krause, M., Lucks, S.: Improved cryptanalysis of the self-shrinking generator. In: Varadharajan, V., Mu, Y. (eds.) ACISP 2001. LNCS, vol. 2119, pp. 21–35. Springer, Heidelberg (2001)
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Hell, M., Johansson, T. (2005). Some Attacks on the Bit-Search Generator. In: Gilbert, H., Handschuh, H. (eds) Fast Software Encryption. FSE 2005. Lecture Notes in Computer Science, vol 3557. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11502760_14
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DOI: https://doi.org/10.1007/11502760_14
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