A digital random-number generator is developed and implemented based on the discrete chaotic-signal algorithm. The digital generator employs the matrix method of chaotic-signal synthesis. The sequence of 8-bit numbers produced by the digital generator is determined by a set of initial data, a variety of versions of which are stored in the generator's read-only memory. Switching the set of initial conditions in accordance with a predetermined protocol can be used to dynamically change the password. The digital generator is intended to operate as a coder-decoder in communications systems with wideband chaotic signals.