A high-speed pseudo-random number generator comprising a first shift register with p stages for storing and shifting a value with the least significant bit being adjacent an output terminal; a second shift register with b stages for storing and shifting a pre-loaded value with the least significant bit of the pre-loaded value being stored in the bth stage; a serial adder having at least l input taps with the serial adder adding the two values shifted out of the first and second shift registers and loading the sum output of the serial adder into the first shift register; and a controller for controlling clocking of the first and second shift registers and the serial adder, controlling pre-loading of the pre-load value into the second shift register, and clearing the serial adder.