Blind Synchronization of m-Sequences with Even Span

The problem of recovering the phase on a known binary m-sequence that is corrupted by a binary noise source is considered. This problem arises in the cryptanalysis of stream ciphers formed from a nonlinear combination of m-sequences. A synchronization procedure is developed for even span n. The procedure obtains a reliable estimate of the phase of an m-sequence of span n from unreliable estimates of the phases of a small number of shifts of a fixed m-sequence of span n/2. These latter estimates can be obtained from a variety of methods available in the literature. The procedure results in a reduction of complexity but requires observing on the order of the square root of the m-sequence’s period.