A compact microelectronic device for performing modular multiplication and exponentiation over large numbers

A compact synchronous microelectronic peripheral machine for standard microprocessors with means for proper clocking and control, has as essential elements: three main subdivided, switched and clocked shift registers, B, S, and N; two only multiplexed serial/parallel multipliers; borrow detectors, ancillary subtractors and adders; delay registers and switching elements; all of which embody a totally integrated concurrent and synchronous process approach to modular multiplication, squaring, and exponentiation. A method for carrying out modular multiplication, wherein the multiplicand A , the multiplier B and the modul, N, comprise m characters of k bits each, the multiplier not being greater than the modulus, is also described, wherein the multiplicand can be much larger than the modulus. It is demonstrated how the device can be used as a large number processor in the normal field of numbers.