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2015 | OriginalPaper | Chapter

Some Results Using the Matrix Methods on Impossible, Integral and Zero-Correlation Distinguishers for Feistel-Like Ciphers

Authors : Thierry P. Berger, Marine Minier

Published in: Progress in Cryptology -- INDOCRYPT 2015

Publisher: Springer International Publishing

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Abstract

While many recent publications have shown strong relations between impossible differential, integral and zero-correlation distinguishers for SPNs and Feistel-like ciphers, this paper tries to bring grist to the mill to this research direction by first, studying the Type-III, the Source-Heavy (SH) and the Target-Heavy (TH) Feistel-like ciphers regarding those three kinds of distinguishers. Second, this paper tries to make a link between the matrix methods used to find such distinguishers and the adjacency matrix of the graph of a Feistel-like cipher.

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Appendix
Available only for authorised users
Footnotes
1
We refer to [5] for the complete table describing the XOR effect in the matrix method.
 
2
In particular a coefficient 2 could not appear due to the restricted previous definition where a receiver could not receive twice.
 
Literature
1.
go back to reference Arnault, F., Berger, T.P., Minier, M., Pousse, B.: Revisiting LFSRs for cryptographic applications. IEEE Trans. Inf. Theory 57(12), 8095–8113 (2011)MathSciNetCrossRef Arnault, F., Berger, T.P., Minier, M., Pousse, B.: Revisiting LFSRs for cryptographic applications. IEEE Trans. Inf. Theory 57(12), 8095–8113 (2011)MathSciNetCrossRef
2.
go back to reference Berger, T.P., Minier, M., Thomas, G.: Extended generalized feistel networks using matrix representation. In: Lange, T., Lauter, K., Lisoněk, P. (eds.) SAC 2013. LNCS, vol. 8282, pp. 289–305. Springer, Heidelberg (2014) CrossRef Berger, T.P., Minier, M., Thomas, G.: Extended generalized feistel networks using matrix representation. In: Lange, T., Lauter, K., Lisoněk, P. (eds.) SAC 2013. LNCS, vol. 8282, pp. 289–305. Springer, Heidelberg (2014) CrossRef
3.
go back to reference Biham, E., Biryukov, A., Shamir, A.: Cryptanalysis of Skipjack reduced to 31 rounds using impossible differentials. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 12–23. Springer, Heidelberg (1999) Biham, E., Biryukov, A., Shamir, A.: Cryptanalysis of Skipjack reduced to 31 rounds using impossible differentials. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 12–23. Springer, Heidelberg (1999)
4.
go back to reference Blondeau, C., Bogdanov, A., Wang, M.: On the (In)equivalence of impossible differential and zero-correlation distinguishers for Feistel- and Skipjack-type ciphers. In: Boureanu, I., Owesarski, P., Vaudenay, S. (eds.) ACNS 2014. LNCS, vol. 8479, pp. 271–288. Springer, Heidelberg (2014) Blondeau, C., Bogdanov, A., Wang, M.: On the (In)equivalence of impossible differential and zero-correlation distinguishers for Feistel- and Skipjack-type ciphers. In: Boureanu, I., Owesarski, P., Vaudenay, S. (eds.) ACNS 2014. LNCS, vol. 8479, pp. 271–288. Springer, Heidelberg (2014)
5.
go back to reference Blondeau, C., Minier, M.: Analysis of impossible, integral and zero-correlation attacks on type-ii generalized Feistel networks using the matrix method. In: Leander, G. (ed.) FSE 2015. LNCS, vol. 9054, pp. 92–113. Springer, Heidelberg (2015) CrossRef Blondeau, C., Minier, M.: Analysis of impossible, integral and zero-correlation attacks on type-ii generalized Feistel networks using the matrix method. In: Leander, G. (ed.) FSE 2015. LNCS, vol. 9054, pp. 92–113. Springer, Heidelberg (2015) CrossRef
6.
go back to reference Blondeau, C., Minier, M.: Relations between Impossible, Integral and Zero-correlation Key-Recovery Attacks (extended version). Cryptology ePrint Archive, Report 2015/141 (2015). http://eprint.iacr.org/ Blondeau, C., Minier, M.: Relations between Impossible, Integral and Zero-correlation Key-Recovery Attacks (extended version). Cryptology ePrint Archive, Report 2015/141 (2015). http://​eprint.​iacr.​org/​
7.
go back to reference Bogdanov, A., Leander, G., Nyberg, K., Wang, M.: Integral and multidimensional linear distinguishers with correlation zero. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 244–261. Springer, Heidelberg (2012) CrossRef Bogdanov, A., Leander, G., Nyberg, K., Wang, M.: Integral and multidimensional linear distinguishers with correlation zero. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 244–261. Springer, Heidelberg (2012) CrossRef
8.
go back to reference Bogdanov, A., Rijmen, V.: Zero-correlation linear cryptanalysis of block ciphers. IACR Cryptology ePrint Arch. 2011, 123 (2011) Bogdanov, A., Rijmen, V.: Zero-correlation linear cryptanalysis of block ciphers. IACR Cryptology ePrint Arch. 2011, 123 (2011)
9.
go back to reference Bouillaguet, C., Dunkelman, O., Fouque, P.-A., Leurent, G.: New insights on impossible differential cryptanalysis. In: Miri, A., Vaudenay, S. (eds.) SAC 2011. LNCS, vol. 7118, pp. 243–259. Springer, Heidelberg (2012) CrossRef Bouillaguet, C., Dunkelman, O., Fouque, P.-A., Leurent, G.: New insights on impossible differential cryptanalysis. In: Miri, A., Vaudenay, S. (eds.) SAC 2011. LNCS, vol. 7118, pp. 243–259. Springer, Heidelberg (2012) CrossRef
10.
go back to reference Kim, J.-S., Hong, S.H., Sung, J., Lee, S.-J., Lim, J.-I., Sung, S.H.: Impossible differential cryptanalysis for block cipher structures. In: Johansson, T., Maitra, S. (eds.) INDOCRYPT 2003. LNCS, vol. 2904, pp. 82–96. Springer, Heidelberg (2003) CrossRef Kim, J.-S., Hong, S.H., Sung, J., Lee, S.-J., Lim, J.-I., Sung, S.H.: Impossible differential cryptanalysis for block cipher structures. In: Johansson, T., Maitra, S. (eds.) INDOCRYPT 2003. LNCS, vol. 2904, pp. 82–96. Springer, Heidelberg (2003) CrossRef
11.
go back to reference Knudsen, L.: DEAL-a 128-bit block cipher. Complexity 258(2), 216 (1998) Knudsen, L.: DEAL-a 128-bit block cipher. Complexity 258(2), 216 (1998)
13.
go back to reference Knudsen, L.R., Wagner, D.: Integral cryptanalysis. In: Daemen, J., Rijmen, V. (eds.) FSE 2002. LNCS, vol. 2365, pp. 112–127. Springer, Heidelberg (2002) CrossRef Knudsen, L.R., Wagner, D.: Integral cryptanalysis. In: Daemen, J., Rijmen, V. (eds.) FSE 2002. LNCS, vol. 2365, pp. 112–127. Springer, Heidelberg (2002) CrossRef
14.
go back to reference Luo, Y., Lai, X., Wu, Z., Gong, G.: A unified method for finding impossible differentials of block cipher structures. Inf. Sci. 263, 211–220 (2014)CrossRef Luo, Y., Lai, X., Wu, Z., Gong, G.: A unified method for finding impossible differentials of block cipher structures. Inf. Sci. 263, 211–220 (2014)CrossRef
15.
go back to reference Soleimany, H., Nyberg, K.: Zero-correlation linear cryptanalysis of reduced-round LBlock. Des. Codes Crypt. 73(2), 683–698 (2014)MATHMathSciNetCrossRef Soleimany, H., Nyberg, K.: Zero-correlation linear cryptanalysis of reduced-round LBlock. Des. Codes Crypt. 73(2), 683–698 (2014)MATHMathSciNetCrossRef
16.
go back to reference Sun, B., Liu, Z., Rijmen, V., Li, R., Cheng, L., Wang, Q., Alkhzaimi, H., Li, C.: Links among impossible differential, integral and zero correlation linear cryptanalysis. Cryptology ePrint Archive, Report 2015/181 (2015). http://eprint.iacr.org/ Sun, B., Liu, Z., Rijmen, V., Li, R., Cheng, L., Wang, Q., Alkhzaimi, H., Li, C.: Links among impossible differential, integral and zero correlation linear cryptanalysis. Cryptology ePrint Archive, Report 2015/181 (2015). http://​eprint.​iacr.​org/​
17.
go back to reference Sun, B., Liu, Z., Rijmen, V., Li, R., Cheng, L., Wang, Q., Alkhzaimi, H., Li, C.: Links among impossible differential, integral and zero correlation linear cryptanalysis. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015, Part I. LNCS, vol. 9215, pp. 95–115. Springer, Heidelberg (2015) CrossRef Sun, B., Liu, Z., Rijmen, V., Li, R., Cheng, L., Wang, Q., Alkhzaimi, H., Li, C.: Links among impossible differential, integral and zero correlation linear cryptanalysis. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015, Part I. LNCS, vol. 9215, pp. 95–115. Springer, Heidelberg (2015) CrossRef
18.
go back to reference Suzaki, T., Minematsu, K.: Improving the generalized Feistel. In: Hong, S., Iwata, T. (eds.) FSE 2010. LNCS, vol. 6147, pp. 19–39. Springer, Heidelberg (2010) CrossRef Suzaki, T., Minematsu, K.: Improving the generalized Feistel. In: Hong, S., Iwata, T. (eds.) FSE 2010. LNCS, vol. 6147, pp. 19–39. Springer, Heidelberg (2010) CrossRef
19.
go back to reference Wu, S., Wang, M.: Automatic search of truncated impossible differentials for word-oriented block ciphers. In: Galbraith, S., Nandi, M. (eds.) INDOCRYPT 2012. LNCS, vol. 7668, pp. 283–302. Springer, Heidelberg (2012) CrossRef Wu, S., Wang, M.: Automatic search of truncated impossible differentials for word-oriented block ciphers. In: Galbraith, S., Nandi, M. (eds.) INDOCRYPT 2012. LNCS, vol. 7668, pp. 283–302. Springer, Heidelberg (2012) CrossRef
20.
go back to reference Yanagihara, S., Iwata, T.: Improving the permutation layer of type 1, type 3, source-heavy, and target-heavy generalized Feistel structures. IEICE Trans. 96–A(1), 2–14 (2013)CrossRef Yanagihara, S., Iwata, T.: Improving the permutation layer of type 1, type 3, source-heavy, and target-heavy generalized Feistel structures. IEICE Trans. 96–A(1), 2–14 (2013)CrossRef
21.
go back to reference Zhang, W., Su, B., Wu, W., Feng, D., Wu, C.: Extending higher-order integral: an efficient unified algorithm of constructing integral distinguishers for block ciphers. In: Bao, F., Samarati, P., Zhou, J. (eds.) ACNS 2012. LNCS, vol. 7341, pp. 117–134. Springer, Heidelberg (2012) CrossRef Zhang, W., Su, B., Wu, W., Feng, D., Wu, C.: Extending higher-order integral: an efficient unified algorithm of constructing integral distinguishers for block ciphers. In: Bao, F., Samarati, P., Zhou, J. (eds.) ACNS 2012. LNCS, vol. 7341, pp. 117–134. Springer, Heidelberg (2012) CrossRef
Metadata
Title
Some Results Using the Matrix Methods on Impossible, Integral and Zero-Correlation Distinguishers for Feistel-Like Ciphers
Authors
Thierry P. Berger
Marine Minier
Copyright Year
2015
DOI
https://doi.org/10.1007/978-3-319-26617-6_10

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