ABSTRACT
The basic arithmetic operations (i.e., addition, multiplication, and inversion)
in prime and binary extension fields, GF(p) and GF(2n), have several applications in cryptography, such as RSA algorithm, Diffie-Hellman key
exchange algorithm [1], the U.S. federal Digital Signature Standard [2], and
also elliptic and hyperelliptic curve cryptography [3,4]. Efficient calculation
of multiplicative inverses of elements in both fields is of utmost importance
since inversion is the most time-consuming operation in hyperelliptic curve
cryptography when affine coordinates are selected [5-10].
