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Nonlinear Equivalence of Stream Ciphers

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Part of the Lecture Notes in Computer Science book series (LNSC,volume 6147)


In this paper we investigate nonlinear equivalence of stream ciphers over a finite field, exemplified by the pure LFSR-based filter generator over \(\mathbb{F}_2\). We define a nonlinear equivalence class consisting of filter generators of length n that generate a binary keystream of period dividing 2n − 1, and investigate certain cryptographic properties of the ciphers in this class. We show that a number of important cryptographic properties, such as algebraic immunity and nonlinearity, are not invariant among elements of the same equivalence class. It follows that analysis of cipher-components in isolation presents some limitations, as it most often involves investigating cryptographic properties that vary among equivalent ciphers. Thus in order to assess the resistance of a cipher against a certain type of attack, one should in theory determine the weakest equivalent cipher and not only a particular instance. This is however likely to be a very difficult task, when we consider the size of the equivalence class for ciphers used in practice; therefore assessing the exact cryptographic properties of a cipher appears to be notoriously difficult.


  • Stream ciphers
  • sequences
  • nonlinear equivalence


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Rønjom, S., Cid, C. (2010). Nonlinear Equivalence of Stream Ciphers. In: Hong, S., Iwata, T. (eds) Fast Software Encryption. FSE 2010. Lecture Notes in Computer Science, vol 6147. Springer, Berlin, Heidelberg.

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  • Print ISBN: 978-3-642-13857-7

  • Online ISBN: 978-3-642-13858-4

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