Multiplier architectures for GF(p) and GF(2/sup n/)

Two new hardware architectures are proposed for performing multiplication in GF(p) and GF (2/sup n/), which are the most time-consuming operations in many cryptographic applications. The architectures provide very fast and efficient execution of multiplication in both GF(p) and GF(2/sup n/), and can be mainly used in elliptic curve cryptography. Both architectures are scalable and therefore can handle operands of any size. They can be configured to the available area and/or desired performance. The algorithm implemented in the architectures is the Montgomery multiplication algorithm which proved to be very efficient in both fields. The first architecture utilises a precomputation technique that reduces the critical path delay at the expense of using extra logic, which has a limited negative impact on the silicon area for operand precisions of cryptographic interest. The second architecture computes multiplication faster in GF(2/sup n/) than GF(p), which conforms with the premise of GF(2/sup n/) for hardware realisations. Both architectures provide new alternatives that offer faster computation of multiplication and useful features.