Nonlinear Equivalence of Stream Ciphers

  • Sondre Rønjom
  • Carlos Cid
Conference paper

DOI: 10.1007/978-3-642-13858-4_3

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6147)
Cite this paper as:
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


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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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Sondre Rønjom
    • 1
  • Carlos Cid
    • 2
  1. 1.Crypto Technology GroupNorwegian National Security AuthorityBærumNorway
  2. 2.Information Security GroupRoyal Holloway, University of LondonEghamUnited Kingdom

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