New Correlations of RC4 PRGA Using Nonzero-Bit Differences

  • Authors:
  • Atsuko Miyaji;Masahiro Sukegawa

  • Affiliations:
  • Japan Advanced Institute of Science and Technology,;Japan Advanced Institute of Science and Technology,

  • Venue:
  • ACISP '09 Proceedings of the 14th Australasian Conference on Information Security and Privacy
  • Year:
  • 2009

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Abstract

RC4 is the stream cipher proposed by Rivest in 1987, which is widely used in a number of commercial products because of its simplicity and substantial security. RC4 exploits shuffle-exchange paradigm, which uses a permutation S . Many attacks have been reported so far. No study, however, has focused on correlations in the Pseudo-Random Generation (PRGA) between two permutations S and S *** with some differences, nevertheless such correlations are related to an inherent weakness of shuffle-exchange-type PRGA. In this paper, we investigate the correlations between S and S *** with some differences in the initial round. We show that correlations between S and S *** remain before $``i"$ is in the position where the nonzero-bit difference exists in the initial round, and that the correlations remain with non negligible probability even after $``i"$ passed by the position. This means that the same correlations between S and S *** will be observed after the 255-th round. This reveals an inherent weakness of shuffle-exchange-type PRGA.