On the design of reconfigurable multipliers for integer and Galois field multiplication
Microprocessors & Microsystems
Extended sequential logic for synchronous circuit optimization and its applications
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
A fast finite field multiplier
ARC'07 Proceedings of the 3rd international conference on Reconfigurable computing: architectures, tools and applications
Toward a solution of the reverse engineering problem using FPGAs
Euro-Par'06 Proceedings of the CoreGRID 2006, UNICORE Summit 2006, Petascale Computational Biology and Bioinformatics conference on Parallel processing
On efficient implementation of accumulation in finite field over GF(2m) and its applications
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Low-power and high-speed design of a versatile bit-serial multiplier in finite fields GF(2m)
Integration, the VLSI Journal
Utilization of Pipeline Technique in AOP Based Multipliers with Parallel Inputs
Journal of Signal Processing Systems
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Arithmetic operations over finite fields GF(2^m) are widely used in cryptography, error-correcting codes and signal processing. In particular, multiplication is especially relevant since other arithmetic operators, such as division or exponentiation, which they usually utilize multipliers as building blocks. Hardware implementation of field multiplication may provide a great speedup in procedure's performance, which easily exceeds the one observed in software platforms. In this paper we deal with an FPGA implementation of an efficient serial multiplier over the binary extension fields GF(2^193) and GF(2^239). Those extension fields are included among the ones recommended by NIST (National Institute of Standards and Technology) standards for Elliptic Curve Cryptography. Our multiplier is of type Serial/Parallel LSB-first and operates with a latency of m-clock cycles, where m is the length of the field word. We calculate the space complexity attending the number of slices used in the FPGA.