Abstract
By using the theory of finite field Fourier transforms, the subject of nonlinear filters of m-sequences is described in a language familiar to the field of signal processing. The most important use of spectral techniques in the design of nonlinear filters is summarized. Many classes of nonlinear filters are given a spectral interpretation and nonlinear filters with right cryptographic properties are described. In particular, the steps to obtain nonlinear filters with large linear complexity and period are shown.
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References
Blahut, R.E.: Transform Techniques for Error Control Codes. IBM J. Res. Develop. 23(3) (May 1979)
Chepyzhov, V., Smeets, B.: On a Fast Correlation Attack on Certain Stream Ciphers. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 176–185. Springer, Heidelberg (1991)
Fúster-Sabater, A., García-Villalba, L.J.: Likelihood that a Pseudorandom Sequence Generator has Optimal Properties. Electronics Letters 34, 646–647 (1998)
Fúster-Sabater, A., García-Villalba, L.J.: An Efficient Algorithm to Generate Binary Sequences for Cryptographic Purposes. Theoretical Computer Science 259, 679–688 (2001)
García-Villalba, L.J., Fúster-Sabater, A.: On the General Classification of Nonlinear Filters of m-Sequences. Information Processing Letters 69, 227–232 (1999)
García-Villalba, L.J., Fúster-Sabater, A.: On the Linear Complexity of the Sequences Generated by Nonlinear Filterings. Information Processing Letters 76, 67–73 (2000)
García-Villalba, L.J., Rodríguez-Palánquex, M.C.: A Family of Keystream Generators with Large Linear Complexity. Applied Mathematics Letters 14, 545–547 (2001)
García-Villalba, L.J.: On the Number of Equivalence Classes in Certain Stream Ciphers. In: Kumar, V., Gavrilova, M.L., Tan, C.J.K., L’Ecuyer, P. (eds.) ICCSA 2003. LNCS, vol. 2669, pp. 129–138. Springer, Heidelberg (2003)
Golomb, S.W.: Shift Register-Sequences. Aegean Park Press, California (1982)
Groth, E.J.: Generation of Binary Sequences with Controllable Complexity. IEEE Trans. Inform. Theory IT-17 (May 1971)
Johansson, T., Jönsson, F.: Improved Fast Correlation Attacks on Stream Ciphers via Convolutional Codes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 347–362. Springer, Heidelberg (1999)
Johansson, T., Jönsson, F.: Fast Correlation Attacks Based on Turbo Codes Techniques. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 181–197. Springer, Heidelberg (1999)
Key, E.L.: An Analysis of the Structure and Complexity of Non-Linear Binary Sequence Generators. IEEE Trans. Inform. Theory IT-22(6), 732–736 (1976)
Kumar, P.V., Scholtz, R.A.: Bounds on the Linear Span of Bent Sequences. IEEE Trans. Inform. Theory IT-29, 854–862 (1983)
Lidl, R., Niederreiter, H.: Introduction to Finite Fields and Their Applications. Cambridge University Press, Cambridge (1986)
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.: Fast Correlation Attacks on Stream Ciphers. J. Cryptology, 159–176 (1989)
Meier, W., Staffelback, O.: Nonlinearity Criteria for Cryptographic Functions. In: Quisquater, J.-J., Vandewalle, J. (eds.) EUROCRYPT 1989. LNCS, vol. 434, pp. 549–562. Springer, Heidelberg (1990)
Mihaljevic, M.J., Golic, J.D.: A Fast Iterative Algorithm for a Shift Register Initial State Reconstruction Given the Noisy Output Sequence. In: Seberry, J., Pieprzyk, J.P. (eds.) AUSCRYPT 1990. LNCS, vol. 453, pp. 165–175. Springer, Heidelberg (1990)
Mihaljevic, M.J., Golic, J.D.: A Comparison of Cryptanalytic Principles Based on Iterative Error-Correction. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 527–531. Springer, Heidelberg (1991)
Penzhorn, W.T., Kühn, G.J.: Computation of Low-Weight Parity Checks for Correlation Attacks on Stream Ciphers. In: Boyd, C. (ed.) Cryptography and Coding 1995. LNCS, vol. 1025, pp. 74–83. Springer, Heidelberg (1995)
Penzhorn, W.T.: Correlation Attacks on Stream Ciphers: Computing Low-Weight Parity Checks Based on Error-Correcting Codes. In: Gollmann, D. (ed.) FSE 1996. LNCS, vol. 1039, pp. 159–172. Springer, Heidelberg (1996)
Rueppel, R.A.: Analysis and Design of Stream Ciphers. Springer, New York (1986)
Simmons, G.J.: Contemporary Cryptology: The Science of Information Integrity. IEEE Press, Los Alamitos (1991)
Siegenthaler, T.: Decrypting a Class of Stream Ciphers Using Ciphertext Only. IEEE Trans. Computers C-34(1), 81–84 (1985)
van Tilborg, H.C.A.: Fundamentals of Cryptology. Kluwer Academic Publishers, Dordrecht (2000)
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Villalba, L.J.G. (2004). Use of Spectral Techniques in the Design of Symmetrical Cryptosystems. In: Laganá, A., Gavrilova, M.L., Kumar, V., Mun, Y., Tan, C.J.K., Gervasi, O. (eds) Computational Science and Its Applications – ICCSA 2004. ICCSA 2004. Lecture Notes in Computer Science, vol 3043. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24707-4_99
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DOI: https://doi.org/10.1007/978-3-540-24707-4_99
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