Reconfigurable implementation of karatsuba multiplier for Galois field in elliptic curves

Abstract

The efficiency of the core Galois field arithmetic improves the performance of elliptic curve based public key cryptosystem implementation. This paper describes the design and implementation of a reconfigurable Galois field multiplier, which is implemented using field programmable gate arrays (FPGAs). The multiplier of Galois field based on karatsuba's divide and conquer algorithm allows for reasonable speedup of the top-level public key algorithms. Binary Karatsuba multiplier is more efficient if it is truncated at n-bit multiplicand level and use an efficient classic multiplier algorithm. In these work three levels to truncate Binary karatsuba algorithm (4 bits, 8 bits and 16 bits) are chosen showing that 8 bits is the best level for minimum number of slices and time delay to truncate Binary karatsuba algorithm which is designed on a Xilinx VirtexE XCV2600 FPGA device. The VHDL hardware models are building using Xilinx ISE foundation software. This work is able to compute GF(2191) multiplication in 45.889 ns. © 2010 Springer Science+Business Media B.V.