Architectures for unified field inversion with applications in elliptic curve cryptography

We present two new inversion algorithms for binary extension and prime fields, which are slightly modified versions of the Montgomery inverse algorithm. A hardware architecture implementing these algorithms is also introduced. In our proposed architecture, the field elements are represented using a multi-word format which allows a scalable and unified architecture to operate in a broad range of precision. This hardware architecture can be used to obtain efficient implementations of elliptic curve cryptography primitives.