Statistical Weakness of Multiplexed Sequences,

It is proved that the out-of-phase autocorrelation of a well-known class of multiplexed sequences for cryptographic and spread spectrum applications is necessarily high for relatively small values of the phase shifts. Related design criteria for the multiplexer generator including the use of full positive difference sets are proposed. By generalizing the classical occupancy problem, higher order statistical weaknesses of multiplexed sequences are also established.