ABSTRACT
In this final chapter, we discuss the use of the double-base number system (DBNS) in performing exponentiation over finite fields, in particular, Galois fields, since the importance of fast exponentiation over such fields for modern cryptography is very high. The most famous and widely used cryptosystem, RSA [1], and many other number theoretic systems [2–7] rely on the existence of fast methods for exponentiation, and a large variety of techniques can be found in the literature. Although deeply studied, this computational operation still possesses some unknown features, the solutions of which might have a significant impact on the efficient performance of many cryptosystems.
