Reconfigurable Architecture for Elliptic Curve Cryptography Using FPGA

Algorithm 1

Bit-level multiplication algorithm for GF(2^𝑚).

  Input: 𝐴, 𝐵  𝜖 GF(2^𝑚)

  Output: 𝐷=(𝐷₀,𝐷₁,𝐷₂,…,𝐷_𝑚−1)  𝜖 GF(2^𝑚), 𝐷=𝐴⋅𝐵

(1) For 0≤𝑡≤𝑚−1

(2) For 0≤𝑠≤𝑚−1

(3) 𝐷_𝑠+𝑡+1←𝑦_𝑠,𝑠+1

(4) end for

(5) end for

(6) return 𝐷