Wu and Hasar discuss the exponentiation of a root in GF(2^m). The Galois field representation is useful in cryptography, so this work has immediate applications in network messaging. Public key encryption and decryption, which are in wide use today, require exponentiation.

The paper is very mathematical, including theorems, lemmas, and the introduction and manipulation of symbols, but it is also applied, including example circuit diagrams and the presentation of directly codable algorithms. The use of the radix-4 signed digit (SD-radix4) representation improves the efficiency of the exponentiation operation in GF(2^m).

The authors’ primary claim is that the operations required to exponentiate in GF(2^m) are more efficient in the SD-radix4 representation. Mathematical, algorithmic, and hardware details necessary for the implementation of the exponentiation and for the support of this thesis are given.

This is a very specific result; there is no claim to generality for this approach or for the representation of numbers in SD-radix4. Those who are interested in the efficient implementation of encryption procedures will find this rewarding reading.