A flexible soft IP core for standard implementations of elliptic curve cryptography in hardware

Elliptic curve cryptography is a rather new, efficient technology for security. However, its implementation is complex and software versions can be prohibitively slow. The main original contribution of this paper is the proposition of a highly parameterizable soft intellectual property core that implements all the operations needed to perform elliptic curve cryptography in hardware. This core supports several standardized elliptic curves. Here, finite field operations use only affine coordinates, which keeps interoperability with software implementations. Also, core operators such as the finite field multiplier and inversion are highly configurable, to enable fulfilling constraints of area or performance, according to what is relevant to each application. The core can thus serve several different purposes, through the setting of parameters that pick the adequate elliptic curve and others that control the finite field multiplier and inversion operator characteristics. Results obtained by synthesizing the core with different parameters for Xilinx FPGAs and 65nm CMOS ASICs show that the exploitable design space is ample: implementations can take from 17 to 5,800μs to execute a point multiplication, taking from 5.7 to 162.2 thousand LUTs in FPGAs or from 16,6 to 360,7 thousand gates in ASICs.