A 193-bit encryption processor for elliptic curve cryptosystem using fast VLSI algorithms in finite fields

We have developed a 193-bit encryption processor elliptic curve (EC) cryptosystem using our proposed finite field VLSI algorithms and architectures, which include an n-times as fast GF multiplier as the serial multiplier, an n-times as fast GF divider as the existing dividers, and an algorithm for the scalar point multiplication. Implementation was made in a prototype with n=2 on a Xilinx FPGA device. The number of clock cycles needed for a scalar point multiplication was 74972, where k was given in SEG2 as the order of the base point on an EC in the 193-bit-wide finite field. We used the irreducible prime polynomial p(x) = x¹⁹³ + x¹⁵ + 1, the EC parameters, and the base point G, which were also given in SEG2.