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A generalized birthday approach for efficiently finding linear relations in l-sequences

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Author

Summary, in English

Feedback with carry shift registers (FCSRs) have previously been available in two configurations, the Fibonacci and Galois architectures. Recently, a generalized and unifying FCSR structure and theory was presented. The new ring FCSR model repairs some weaknesses of the older architectures. Most notably, the carry cell bias property that was exploited for an attack on the eSTREAM final portfolio cipher F-FCSR-H v2 is no longer possible for the updated (and unbroken) F-FCSR-H v3 stream cipher. In this paper we show how to exploit a particular set of linear relations in ring FCSR sequences. We show what biases can be expected, and we also present a generalized birthday algorithm for actually realizing these relations. As all prerequisites of a distinguishing attack are present, we explicitly show a new such attack on F-FCSR-H v3 with an online time complexity of only 2^{37.2}. The offline time complexity (for finding a linear relation) is 2^{56.2}. This is the first successful attack on F-FCSR-H v3, the first attack to breach the exhaustive search complexity limit. Note that this attack is completely different from that of F-FCSR-H v2. We focus on this particular application in the paper, but the presented algorithm is actually very general. The algorithm can be applied to any FCSR automaton, so linearly filtered FCSRs and FCSR combiners may be particularly interesting targets for cryptanalysis.

Publishing year

2015

Language

English

Pages

41-57

Publication/Series

Designs, Codes and Cryptography

Volume

74

Issue

1

Document type

Journal article

Publisher

Springer

Topic

  • Electrical Engineering, Electronic Engineering, Information Engineering

Keywords

  • FCSR
  • Linear relations
  • Generalized birthday attack
  • Distinguisher

Status

Published

Research group

  • Crypto and Security

ISBN/ISSN/Other

  • ISSN: 1573-7586