An efficient algorithm for computing modular division over GF(2m) in elliptic curve cryptography

摘要

Modular inversion is the most complicated operation in elliptic curve cryptography(ECC). Based on the Extended Euclidean Algorithm(EEA), this paper presents a modified modular division algorithm in the binary finite field GF(2m). Furthermore, this paper designs a hardware implementation to verify the algorithm's performance with Verilog HDL, we also simulate it in GF(2m) to compare with other algorithms on clock cycles consumption.