A design framework for scalable and unified architectures that perform multiplication in GF(p) and GF(2^m)

The design of multiplication units that are reusable and scalable is of interest for cryptographic applications, where the operand size in bits is usually large, and may significantly change depending on the required level of security or the specific cryptosystem (e.g., RSA or Elliptic Curve). The use of the Montgomery multiplication (MM) method combined with techniques for time and space scheduling generates efficient and general solutions in this arena. MM has proven to be useful in both GF(p) and GF(2^m), and opened up the door for unified architectures designed to accommodate both fields. The scalable design does not rely on particular characteristics of the fields, it is adjustable for the silicon area available, and it does not limit the precision of the operands (variable precision). This way, the design lasts longer. This paper presents a generalization of the concept of scalable and unified architectures for multiplication in GF(p) and GF(2^m). A design framework is initially presented, and followed by a design example of a radix-8 processing element for a scalable and unified MM architecture. Experimental results show the potential of this method.