Breaking Elliptic Curve Cryptosystems Using Reconfigurable Hardware

This paper reports a new speed record for FPGAs in cracking Elliptic Curve Cryptosystems. We conduct a detailed analysis of different F
_2(m)
multiplication approaches in this application. A novel architecture using optimized normal basis multipliers is proposed to solve the Certicom challenge ECC2K-130. We compare the FPGA performance against CPUs, GPUs, and the Sony PlayStation 3. Our implementations show low-cost FPGAs outperform even multicore desktop processors and graphics cards by a factor of 2.