Some remarks on FCSRs and implications for stream ciphers

Simon Fischer 1 , Willi Meier 2  and Dirk Stegemann 3
  • 1 Siemens AG, Zug, Switzerland. Email:
  • 2 FHNW, Windisch, Switzerland. Email:
  • 3 University of Mannheim, Mannheim, Germany. Email:


Feedback with carry shift registers (FCSRs) are extensively discussed in the context of pseudorandom number generation and as building blocks for stream ciphers. Similarly to linear feedback shift registers, FCSRs may be represented in Galois and in Fibonacci architecture. We describe the first formal characterization of periodic Galois states and show an efficient mapping between periodic Galois states and periodic Fibonacci states. Additionally we provide a method for explicitly computing the autocorrelation of maximum-period FCSR sequences and discuss the impact of our findings on the design of FCSR-based stream ciphers.

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JMC is a forum for original research articles in the area of mathematical cryptology. Works in the theory of cryptology and articles linking mathematics with cryptology are welcome. Submissions from all areas of mathematics significant for cryptology are published, including but not limited to, algebra, algebraic geometry, coding theory, combinatorics, number theory, probability and stochastic processes.