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We investigate theoretically and experimentally the detrimental effect of fiber dispersion on the synchronization of an optoelectronic phase chaos cryptosystem. We evaluate the root-mean square synchronization error and the cancellation spectra between the emitter and the receiver in order to characterize the quality of the optical fiber communication link. These two indicators explicitly show in temporal and spectral domain how fiber dispersion does negatively affect the phase chaos cancellation at the receiver stage. We demonstrate that the dispersion management techniques used in conventional optical fiber networks, such as dispersion-compensating modules/fibers or dispersion shifted fibers, are also efficient to strongly reduce the detrimental effects of fiber propagation in phase chaos communications. This compatibility therefore opens the way to a successful integration of more than 10-Gb/s phase chaos communications systems in existing networks, even when the fiber link spans over more than 100 km.