Minimum-clock-cycle Itoh-Tsujii algorithm hardware implementation for cryptography applications over GF(2m) fields

Inversion over finite fields is the most costly basic operation for diverse cryptographic applications, such as elliptic curve cryptography and others. The Itoh-Tsujii algorithm (ITA) provides high performance implementations for the inversion operation in standard bases through diverse versions like squarer-ITA, parallel squarer-ITA or quad-ITA. A new modification of the ITA algorithm allows the inversion over finite fields in a minimal number of clock cycles. The proposed implementations complete the inversion over GF(2²³³) or GF(2⁴⁰⁹) from only 10 clock cycles.