The Vulnerability of Geometric Sequences Based on Fields of Odd Characteristic

Journal of Cryptology 7 (1994) 33-51.

Andrew Klapper, 779A Anderson Hall, Dept. of Computer Science, University of Kentucky, Lexington, KY, 40506-0046, klapper at

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.

Index Terms -- Cryptanalysis, binary sequence, geometric sequence, linear complexity, Galois field.