A multidimensional linear distinguishing attack on the Shannon cipher

In this article, we present a linear distinguishing attack on the stream cipher Shannon. Our distinguisher can distinguish the output keystream of Shannon from about 2107 keystream words while using an array of 232 counters. The distinguisher makes use of a multidimensional linear transformation instead of a 1D transformation, which is traditionally used in linear distinguishing attacks. This gives a clear improvement to the keystream requirement: we need approximately 25 times less keystream than when a 1D transformation is used. In addition, we give evidence of the correctness of the distinguisher by applying it to a smaller version of Shannon.