Geodesic
A related-key attack on iterated chaotic ciphers
Kybernetika, Tome 44 (2008) no. 4, pp. 501-510.

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In this paper, we present a new type of attack on iterated chaotic ciphers using related keys. Based on the fact that a chaotic sequence is not sensitive to the less significant bits of initial conditions and parameters, a divide- and-conquer attack on iterated chaotic ciphers was presented by us before, which significantly reduces the computing complexity of attacks. However, if the information leaked is significant according to the distribution of the coincidence degrees, a measure for the information leakage of chaotic ciphers, or the size of the key is large, then it is difficult for the divide-and- conquer attack to reduce its computing complexity into a realizable level. The related-key attack we present in this paper simultaneously uses the information leaked from different chaotic sequences generated by related keys and combines the ideas of linear cryptanalysis and divide-and-conquer attack together, hence greatly enhances the efficiency of divide-and-conquer attack. As an example, we test the related-key attack on the ZLL chaotic cipher with a 64-bit key on a Pentium IV 2.5 GHz PC, which takes only 8 minutes and 45 seconds to recover all bits of the key successfully.
Classification : 34C28, 94A60
Keywords: chaotic cipher; related-key attack; ZLL chaotic cipher; divide- and-conquer attack; known plaintexts attack 
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     title = {A related-key attack on iterated chaotic ciphers},
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     pages = {501--510},
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     zbl = {1171.94362},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2008__44_4_a5/}
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Yang, Yang; Jin, Chenhui. A related-key attack on iterated chaotic ciphers. Kybernetika, Tome 44 (2008) no. 4, pp. 501-510. http://geodesic.mathdoc.fr/item/KYB_2008__44_4_a5/