Novel Multiplier Architectures for GF(p) and GF(2^n)E. Savas, A. F. Tenca, M. E. Ciftcibasi, and C. K. KocIEE Proceedings - Computers and Digital Techniques, 151(2):147-160, March 2004.AbstractThis paper proposes two new hardware architectures for performing multiplication in GF(p) and GF(2^n), which is the most time consuming operation in many cryptographic applications. The architectures provide very fast and efficient execution of multiplication in both GF(p) and GF(2^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 Montgomery multiplication algorithm which proved to be very efficient in both fields. The first architecture utilizes 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^n) than GF(p), which conforms with premise of GF(2^n) for hardware realizations. Both architectures provide new alternatives that offer faster computation of multiplication and useful features. |