On the Statistically Optimal Divide and Conquer Correlation Attack on the Shrinking Generator

Shahram Khazaei; Mahmood Salmasizadeh; Javad Mohajeri

Paper 2005/126

On the Statistically Optimal Divide and Conquer Correlation Attack on the Shrinking Generator

Shahram Khazaei, Mahmood Salmasizadeh, and Javad Mohajeri

Abstract

The shrinking generator is a well-known key stream generator composed of two LFSR’s, LFSRx and LFSRc, where LFSRx is clock-controlled according to the regularly clocked LFSRc. In this paper we investigate the minimum required length of the output sequence for successful reconstruction of the LFSRx initial state in an optimal probabilistic divide and conquer correlation attack. We extract an exact expression for the joint probability of the prefix of length m of the output sequence of LFSRx and prefix of length n of the output sequence of the generator. Then we use computer simulation to compare our probability measure and two other probability measures, previousely proposed in [5] and [3], in the sense of minimum required output length. Our simulation results show that our measure reduces the required output length.

Metadata

Available format(s): PDF
Category: Secret-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Keywords: stream ciphers clock-controlled generators shrinking generator divide and conquer attack optimal correlation attacks deletion channel joint probability.
Contact author(s): shahram khazaei @ gmail com
History: 2012-05-19: revised; 2005-04-29: received; See all versions
Short URL: https://ia.cr/2005/126
License: CC BY

BibTeX

@misc{cryptoeprint:2005/126,
      author = {Shahram Khazaei and Mahmood Salmasizadeh and Javad Mohajeri},
      title = {On the Statistically Optimal Divide and Conquer Correlation Attack on the Shrinking Generator},
      howpublished = {Cryptology {ePrint} Archive, Paper 2005/126},
      year = {2005},
      url = {https://eprint.iacr.org/2005/126}
}