International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: A new statistical distinguisher for the shrinking generator

Jovan Dj. Golic
Renato Menicocci
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Abstract: The shrinking generator is a well-known keystream generator composed of two linear feedback shift registers, LFSR$_1$ and LFSR$_2$, where LFSR$_1$ is clock-controlled according to regularly clocked LFSR$_2$. The keystream sequence is thus a decimated LFSR$_1$ sequence. Statistical distinguishers for keystream generators are algorithms whose objective is to distinguish the keystream sequence from a purely random sequence. Previously proposed statistical distinguishers for the shrinking generator are based on detecting binary linear relations in the keystream sequence that hold with a probability sufficiently different from one half. In this paper a novel approach which significantly reduces the required computation time is introduced. It is based on a probabilistic reconstruction of the bits in the regularly clocked LFSR$_1$ sequence that satisfy the LFSR$_1$ recurrence or any linear recurrence derived from low-weight multiples of the LFSR$_1$ characteristic polynomial. The keystream sequence length and the computation time required for a reliable statistical distinction are analyzed both theoretically and experimentally.
  title={A new statistical distinguisher for the shrinking generator},
  booktitle={IACR Eprint archive},
  keywords={secret-key cryptography / cryptanalysis, stream ciphers},
  note={ 12114 received 3 Mar 2003},
  author={Jovan Dj. Golic and Renato Menicocci},