Double-Precision Modular Multiplication Based on a Single-Precision Modular Multiplier and a Standard CPU

We consider the case where double-precision modular multiplications are needed to be performed by a device which contains a custom IC that provides for a single-precision modular multiplication. Such a need can arise, for example, in the cases where security requirements dictate the usage of cryptographic parameters larger than initially expected, or in the cases where a nonexpensive single-precision device is fabricated with the intention of doubling its word size by software means. The presented method is obviously extended to multiplying (k.n) bit operands using an n-bit modular multiplier, for the case where k is a power of 2. Whereas multiprecision modular multiplication is simply executed using an available single-precision modular multiplier which provides external division services, the existence of these services is not assumed in the presented process, as the operation carried by the available modular multiplier is not necessarily based on proper division. The process is controlled by a standard CPU which also performs some simple calculations.