Abstract
Some of the most popular public key encryption algorithms use exponentiation as their core operation, which can be mostly broken into several modular squaring operations. In this paper, we present GF(P)modular squaring algorithms and efficiently implement them on hardware. We present different algorithms, two for squaring and one for reduction combined with the squaring, to provide a general modular squaring algorithm. The algorithms are implemented through datapaths that uses redundant Carry-Save Adders, making the computation time independent form the operands precision. The proposed algorithms are compared with each other as well as with the existing modular squaring algorithms. The experimental results are obtained by synthesizing the hardware designs for FPGA Virtex5 chip (xc5vlx50 - ff1153 technology), which showed interesting results and made our ideas very attractive.