The vulnerability of geometric sequences based on fields of odd characteristic

Abstract

A new method of cryptologic attack on binary sequences is given, using their linear complexities relative to odd prime numbers. We show that, relative to a particular prime number p, the linear complexity of a binary geometric sequences is low. It is also shown that the prime p, can be determined with high probability by a randomized algorithm if a number of bits much smaller than the linear complexity is known. This determination is made by exploiting the imbalance in the number of zeros and ones in the sequences in question, and uses a new statistical measure, the partial imbalance.

Project sponsored by the National Science and Engineering Research Council under grant number OGP0121648, and by the National Security Agency under Grant Number MDA904-91-H-0012. The United States Government is authorized to reproduce and distribute reprints notwithstanding any copyright notation hereon.