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Erschienen in: Cryptography and Communications 3-4/2012

01.12.2012

A survey on fast correlation attacks

verfasst von: Martin Ågren, Carl Löndahl, Martin Hell, Thomas Johansson

Erschienen in: Cryptography and Communications | Ausgabe 3-4/2012

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Abstract

Fast correlation attacks, pioneered by Meier and Staffelbach in 1988, constitute an important class of attacks on stream ciphers. They exploit a correlation between the keystream and the output of a linear feedback shift register (LFSR) within the cipher. Several factors affect the feasibility of such an attack, e.g., the amount of available keystream and the number of taps in the LFSR. Notably, for a fixed number of taps, the length of the LFSR does not affect the complexity of the attack. When the register does not have a sufficiently small number of taps, however, the attacker will try to find parity check equations of low weight, at which point the length of the register does matter. In this paper, we go through the significant contributions to this field of cryptanalysis, reiterating the various algorithms that have been developed for finding parity check equations and performing the online stage on received keystream. We also suggest some new generalizations of Meier-Staffelbach’s original formulations.

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Literatur
1.
Zurück zum Zitat Bahl, L., Cocke, J., Jelinek, F., Raviv, J.: Optimal decoding of linear codes for minimizing symbol error rate. IEEE Trans. Inf. Theory 20(2), 284–287 (1974)MathSciNetMATHCrossRef Bahl, L., Cocke, J., Jelinek, F., Raviv, J.: Optimal decoding of linear codes for minimizing symbol error rate. IEEE Trans. Inf. Theory 20(2), 284–287 (1974)MathSciNetMATHCrossRef
2.
Zurück zum Zitat Berrou, C., Glavieux, A.: Near optimum error correcting and decoding: turbo-codes. IEEE Trans. Commun. 4(10), 1261–1271 (1996)CrossRef Berrou, C., Glavieux, A.: Near optimum error correcting and decoding: turbo-codes. IEEE Trans. Commun. 4(10), 1261–1271 (1996)CrossRef
3.
Zurück zum Zitat Berrou, C., Glavieux, A., Thitimajshima, P.: Near Shannon limit error-correcting coding and decoding. In: Proc., IEEE Int. Conf. on Communications, ICC’93, pp. 1064–1070 (1993) Berrou, C., Glavieux, A., Thitimajshima, P.: Near Shannon limit error-correcting coding and decoding. In: Proc., IEEE Int. Conf. on Communications, ICC’93, pp. 1064–1070 (1993)
4.
Zurück zum Zitat Blum, A., Kalai, A., Wasserman, H.: Noise-tolerant learning, the parity problem, and the statistical query model. In: Yao, F.F., Luks, E.M. (eds.) STOC, pp. 435–440. ACM (2000) Blum, A., Kalai, A., Wasserman, H.: Noise-tolerant learning, the parity problem, and the statistical query model. In: Yao, F.F., Luks, E.M. (eds.) STOC, pp. 435–440. ACM (2000)
5.
Zurück zum Zitat Blum, A., Kalai, A., Wasserman, H.: Noise-tolerant learning, the parity problem, and the statistical query model. J. ACM 50(4), 506–519 (2003)MathSciNetCrossRef Blum, A., Kalai, A., Wasserman, H.: Noise-tolerant learning, the parity problem, and the statistical query model. J. ACM 50(4), 506–519 (2003)MathSciNetCrossRef
6.
Zurück zum Zitat Canteaut, A., Filiol, E. (2002) On the influence of the filtering function on the performance of fast correlation attacks on filter generators. In: Symposium on Information Theory, pp. 299–306 Canteaut, A., Filiol, E. (2002) On the influence of the filtering function on the performance of fast correlation attacks on filter generators. In: Symposium on Information Theory, pp. 299–306
7.
Zurück zum Zitat Canteaut, A., Trabbia, M.: Improved fast correlation attacks using parity-check equations of weight 4 and 5. In: Preneel, B. (ed.) Advances in Cryptology—EUROCRYPT 2000. Lecture Notes in Computer Science, vol. 1807, pp. 573–588. Springer-Verlag (2000) Canteaut, A., Trabbia, M.: Improved fast correlation attacks using parity-check equations of weight 4 and 5. In: Preneel, B. (ed.) Advances in Cryptology—EUROCRYPT 2000. Lecture Notes in Computer Science, vol. 1807, pp. 573–588. Springer-Verlag (2000)
8.
Zurück zum Zitat Chepyzhov, V., Johansson, T., Smeets, B.: A simple algorithm for fast correlation attacks on stream ciphers. In: Schneier, B. (ed.) Fast Software Encryption 2000. Lecture Notes in Computer Science, vol. 1978, pp. 181–195. Springer-Verlag (2000) Chepyzhov, V., Johansson, T., Smeets, B.: A simple algorithm for fast correlation attacks on stream ciphers. In: Schneier, B. (ed.) Fast Software Encryption 2000. Lecture Notes in Computer Science, vol. 1978, pp. 181–195. Springer-Verlag (2000)
9.
Zurück zum Zitat Chepyzhov, V., Smeets, B.: On a fast correlation attack on certain stream ciphers. In: Davies, D.W. (ed.) Advances in Cryptology—EUROCRYPT’91. Lecture Notes in Computer Science, vol. 547, pp. 176–185. Springer-Verlag (1991) Chepyzhov, V., Smeets, B.: On a fast correlation attack on certain stream ciphers. In: Davies, D.W. (ed.) Advances in Cryptology—EUROCRYPT’91. Lecture Notes in Computer Science, vol. 547, pp. 176–185. Springer-Verlag (1991)
10.
Zurück zum Zitat Chose, P., Joux, A., Mitton, M.: Fast correlation attacks: An algorithmic point of view. Lect. Notes Comput. Sci. 2332, 209–221 (2002)MathSciNetCrossRef Chose, P., Joux, A., Mitton, M.: Fast correlation attacks: An algorithmic point of view. Lect. Notes Comput. Sci. 2332, 209–221 (2002)MathSciNetCrossRef
11.
Zurück zum Zitat Coppersmith, D.: Fast evaluation of logarithms in fields of characteristic two. IEEE Trans. Inf. Theory 30(4), 587–594 (1984)MathSciNetMATHCrossRef Coppersmith, D.: Fast evaluation of logarithms in fields of characteristic two. IEEE Trans. Inf. Theory 30(4), 587–594 (1984)MathSciNetMATHCrossRef
12.
Zurück zum Zitat Fossorier, M.P.C., Mihaljevic, M.J., Imai, H.: Reduced complexity iterative decoding of low-density parity check codes based on belief propagation. IEEE Trans. Commun. 47, 673–680 (1999)CrossRef Fossorier, M.P.C., Mihaljevic, M.J., Imai, H.: Reduced complexity iterative decoding of low-density parity check codes based on belief propagation. IEEE Trans. Commun. 47, 673–680 (1999)CrossRef
13.
Zurück zum Zitat Fossorier, M.P.C., Mihaljević, M.J., Imai, H.: Modeling block decoding approaches for the fast correlation attack. IEEE Trans. Inf. Theory 53(12), 4728–4737 (2007)CrossRef Fossorier, M.P.C., Mihaljević, M.J., Imai, H.: Modeling block decoding approaches for the fast correlation attack. IEEE Trans. Inf. Theory 53(12), 4728–4737 (2007)CrossRef
14.
Zurück zum Zitat Fossorier, M.P.C., Mihaljević, M.J. Imai, H., Cui, Y., Matsuura, K.: An algorithm for solving the LPN problem and its application to security evaluation of the HB protocols for RFID authentication. In: Barua, R., Lange, T. (eds.) Progress in Cryptology—INDOCRYPT 2005. Lecture Notes in Computer Science, vol. 4329, pp. 48–62. Springer-Verlag (2006) Fossorier, M.P.C., Mihaljević, M.J. Imai, H., Cui, Y., Matsuura, K.: An algorithm for solving the LPN problem and its application to security evaluation of the HB protocols for RFID authentication. In: Barua, R., Lange, T. (eds.) Progress in Cryptology—INDOCRYPT 2005. Lecture Notes in Computer Science, vol. 4329, pp. 48–62. Springer-Verlag (2006)
16.
Zurück zum Zitat Gallager, R.G.: Low-Density Parity-Check Codes. PhD thesis, MIT Press, Cambridge (1963) Gallager, R.G.: Low-Density Parity-Check Codes. PhD thesis, MIT Press, Cambridge (1963)
17.
Zurück zum Zitat Gilbert, E.N., MacWilliams, F.J., Sloane, N.J.A.: Codes which detect deception. Bell Syst. Tech. J. 53(3), 405–424 (1974)MathSciNetMATH Gilbert, E.N., MacWilliams, F.J., Sloane, N.J.A.: Codes which detect deception. Bell Syst. Tech. J. 53(3), 405–424 (1974)MathSciNetMATH
18.
Zurück zum Zitat Goldreich, O., Rubinfeld, R., Sudan, M.: Learning polynomials with queries: the highly noisy case. In: 36th Annual Symposium on Foundation of Computer Science, pp. 294–303 (1995) Goldreich, O., Rubinfeld, R., Sudan, M.: Learning polynomials with queries: the highly noisy case. In: 36th Annual Symposium on Foundation of Computer Science, pp. 294–303 (1995)
19.
Zurück zum Zitat Golić, J.Dj.: Computation of low-weight parity-check polynomials. Electron. Lett. 32(21), 1981–1982 (1996)CrossRef Golić, J.Dj.: Computation of low-weight parity-check polynomials. Electron. Lett. 32(21), 1981–1982 (1996)CrossRef
20.
Zurück zum Zitat Golić, J.Dj.: Iterative optimum symbol-by-symbol decoding and fast correlation attacks. IEEE Trans. Inf. Theory 47(7), 3040–3049 (2001)MATHCrossRef Golić, J.Dj.: Iterative optimum symbol-by-symbol decoding and fast correlation attacks. IEEE Trans. Inf. Theory 47(7), 3040–3049 (2001)MATHCrossRef
21.
Zurück zum Zitat Hartmann, C.R.P., Rudolph, L.D.: An optimum symbol-by-symbol decoding rule for linear codes. IEEE Trans. Inf. Theory 22(5):514–517 (1976)MathSciNetMATHCrossRef Hartmann, C.R.P., Rudolph, L.D.: An optimum symbol-by-symbol decoding rule for linear codes. IEEE Trans. Inf. Theory 22(5):514–517 (1976)MathSciNetMATHCrossRef
22.
Zurück zum Zitat Johansson, T., Jönsson, F.: Fast correlation attacks based on turbo code techniques. In: Wiener, M.J. (ed.) Advances in Cryptology—CRYPTO’99. Lecture Notes in Computer Science, vol. 1666, pp. 181–197. Springer-Verlag (1999) Johansson, T., Jönsson, F.: Fast correlation attacks based on turbo code techniques. In: Wiener, M.J. (ed.) Advances in Cryptology—CRYPTO’99. Lecture Notes in Computer Science, vol. 1666, pp. 181–197. Springer-Verlag (1999)
23.
Zurück zum Zitat Johansson, T., Jönsson, F.: Improved fast correlation attacks on stream ciphers via convolutional codes. In: Stern, J. (ed.) Advances in Cryptology—EUROCRYPT’99. Lecture Notes in Computer Science, vol. 1592, pp. 347–362. Springer-Verlag (1999) Johansson, T., Jönsson, F.: Improved fast correlation attacks on stream ciphers via convolutional codes. In: Stern, J. (ed.) Advances in Cryptology—EUROCRYPT’99. Lecture Notes in Computer Science, vol. 1592, pp. 347–362. Springer-Verlag (1999)
24.
Zurück zum Zitat Johansson, T., Jönsson, F.: Fast correlation attacks through reconstruction of linear polynomials. In: Bellare, M. (ed.) Advances in Cryptology—CRYPTO 2000. Lecture Notes in Computer Science, vol. 1880, pp. 300–315. Springer-Verlag (2000) Johansson, T., Jönsson, F.: Fast correlation attacks through reconstruction of linear polynomials. In: Bellare, M. (ed.) Advances in Cryptology—CRYPTO 2000. Lecture Notes in Computer Science, vol. 1880, pp. 300–315. Springer-Verlag (2000)
25.
Zurück zum Zitat Jönsson, F.: Some results on fast correlation attacks. PhD thesis, Lund University, Department of Information Technology, P.O. Box 118, SE–221 00, Lund, Sweden (2002) Jönsson, F.: Some results on fast correlation attacks. PhD thesis, Lund University, Department of Information Technology, P.O. Box 118, SE–221 00, Lund, Sweden (2002)
26.
Zurück zum Zitat Levieil, É., Fouque, P.-A.: An improved LPN algorithm. In: De Prisco, R., Yung, M. (eds.) SCN. Lecture Notes in Computer Science, vol. 4116, pp. 348–359. Springer-Verlag (2006) Levieil, É., Fouque, P.-A.: An improved LPN algorithm. In: De Prisco, R., Yung, M. (eds.) SCN. Lecture Notes in Computer Science, vol. 4116, pp. 348–359. Springer-Verlag (2006)
27.
Zurück zum Zitat Meier, W.: Fast correlation attacks: methods and countermeasures. In: Joux, A. (eds.) Fast Software Encryption 2011. Lecture Notes in Computer Science, pp. 55–67. Springer-Verlag (2011) Meier, W.: Fast correlation attacks: methods and countermeasures. In: Joux, A. (eds.) Fast Software Encryption 2011. Lecture Notes in Computer Science, pp. 55–67. Springer-Verlag (2011)
28.
29.
Zurück zum Zitat Mihaljević, M.J., Fossorier, M., Imai, H.: A low-complexity and high-performance algorithm for the fast correlation attack. In: Schneier, B. (ed.) Fast Software Encryption 2000. Lecture Notes in Computer Science, vol. 1978, pp. 196–212. Springer-Verlag (2000) Mihaljević, M.J., Fossorier, M., Imai, H.: A low-complexity and high-performance algorithm for the fast correlation attack. In: Schneier, B. (ed.) Fast Software Encryption 2000. Lecture Notes in Computer Science, vol. 1978, pp. 196–212. Springer-Verlag (2000)
30.
Zurück zum Zitat Mihaljević, M.J., Fossorier, M., Imai, H.: On decoding techniques for cryptanalysis of certain encryption algorithms. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. E84-A, 919–930 (2001) Mihaljević, M.J., Fossorier, M., Imai, H.: On decoding techniques for cryptanalysis of certain encryption algorithms. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. E84-A, 919–930 (2001)
31.
Zurück zum Zitat Mihaljević, M.J., Fossorier, M., Imai, H.: Fast correlation attack algorithm with list decoding and an application. In: Fast Software Encryption 2001. Lecture Notes in Computer Science, vol. 2355, pp. 196–210. Springer-Verlag (2002) Mihaljević, M.J., Fossorier, M., Imai, H.: Fast correlation attack algorithm with list decoding and an application. In: Fast Software Encryption 2001. Lecture Notes in Computer Science, vol. 2355, pp. 196–210. Springer-Verlag (2002)
32.
Zurück zum Zitat Mihaljević, M.J., Golić, J.D.: A fast iterative algorithm for a shift register initial state reconstruction given the noisy output sequence. In: Seberry, J., Pieprzyk, J. (eds.) Advances in Cryptology—AUSCRYPT’90. Lecture Notes in Computer Science, vol. 453, pp. 165–175. Springer-Verlag (1990) Mihaljević, M.J., Golić, J.D.: A fast iterative algorithm for a shift register initial state reconstruction given the noisy output sequence. In: Seberry, J., Pieprzyk, J. (eds.) Advances in Cryptology—AUSCRYPT’90. Lecture Notes in Computer Science, vol. 453, pp. 165–175. Springer-Verlag (1990)
33.
Zurück zum Zitat Molland, H., Mathiassen, J., Helleseth, T.: Improved fast correlation attack using low rate codes. In: Paterson, K. (ed.) Cryptography and Coding—9th IMA Conference. Lecture Notes in Computer Science, vol. 2898, pp. 67–81. Springer Berlin/Heidelberg (2003) Molland, H., Mathiassen, J., Helleseth, T.: Improved fast correlation attack using low rate codes. In: Paterson, K. (ed.) Cryptography and Coding—9th IMA Conference. Lecture Notes in Computer Science, vol. 2898, pp. 67–81. Springer Berlin/Heidelberg (2003)
34.
Zurück zum Zitat Noorkami, M., Fekri, F.: A fast correlation attack via unequal error correcting ldpc codes. In: Okamoto, T. (ed.) Topics in Cryptology—CT-RSA 2004. Lecture Notes in Computer Science, vol. 2964, pp. 54–66 (2004) Noorkami, M., Fekri, F.: A fast correlation attack via unequal error correcting ldpc codes. In: Okamoto, T. (ed.) Topics in Cryptology—CT-RSA 2004. Lecture Notes in Computer Science, vol. 2964, pp. 54–66 (2004)
35.
Zurück zum Zitat Penzhorn, W.T.: Correlation attacks on stream ciphers: computing low weight parity checks based on error correction codes. In: Gollman, D. (ed.) Fast Software Encryption’96. Lecture Notes in Computer Science, vol. 1039, pp. 159–172. Springer-Verlag (1996) Penzhorn, W.T.: Correlation attacks on stream ciphers: computing low weight parity checks based on error correction codes. In: Gollman, D. (ed.) Fast Software Encryption’96. Lecture Notes in Computer Science, vol. 1039, pp. 159–172. Springer-Verlag (1996)
36.
Zurück zum Zitat 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—5th IMA Conference. Lecture Notes in Computer Science, vol. 1025, pp. 74–83. Springer-Verlag (1995) 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—5th IMA Conference. Lecture Notes in Computer Science, vol. 1025, pp. 74–83. Springer-Verlag (1995)
37.
Zurück zum Zitat Siegenthaler, T.: Correlation Attacks on Certain Stream Ciphers with Nonlinear Generators. Presented at IEEE Int. Symp. Inform. Theory, Saint Jovite, Canada, 26–29 Sept. (1983) Siegenthaler, T.: Correlation Attacks on Certain Stream Ciphers with Nonlinear Generators. Presented at IEEE Int. Symp. Inform. Theory, Saint Jovite, Canada, 26–29 Sept. (1983)
38.
Zurück zum Zitat Siegenthaler, T.: Decrypting a class of stream ciphers using ciphertext only. IEEE Trans. Comput. 34, 81–85 (1985)CrossRef Siegenthaler, T.: Decrypting a class of stream ciphers using ciphertext only. IEEE Trans. Comput. 34, 81–85 (1985)CrossRef
39.
Zurück zum Zitat Wagner, D.: A generalized birthday problem. In: Yung, M. (ed.) Advances in Cryptology—CRYPTO 2002. Lecture Notes in Computer Science, vol. 2442, pp. 288–303. Springer-Verlag (2002) Wagner, D.: A generalized birthday problem. In: Yung, M. (ed.) Advances in Cryptology—CRYPTO 2002. Lecture Notes in Computer Science, vol. 2442, pp. 288–303. Springer-Verlag (2002)
40.
Zurück zum Zitat Zhang, B., Feng, D.: Multi-pass fast correlation attack on stream ciphers. In: Biham, E., Youssef, A.M. (eds.) Selected Areas in Cryptography—SAC 2006. Lecture Notes in Computer Science, vol. 4356, pp. 234–248. Springer-Verlag (2007) Zhang, B., Feng, D.: Multi-pass fast correlation attack on stream ciphers. In: Biham, E., Youssef, A.M. (eds.) Selected Areas in Cryptography—SAC 2006. Lecture Notes in Computer Science, vol. 4356, pp. 234–248. Springer-Verlag (2007)
Metadaten
Titel
A survey on fast correlation attacks
verfasst von
Martin Ågren
Carl Löndahl
Martin Hell
Thomas Johansson
Publikationsdatum
01.12.2012
Verlag
Springer US
Erschienen in
Cryptography and Communications / Ausgabe 3-4/2012
Print ISSN: 1936-2447
Elektronische ISSN: 1936-2455
DOI
https://doi.org/10.1007/s12095-012-0062-x

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