Modular exponentiation is core to today's main stream
public key cryptographic systems. In this article, we generalize the
classical fractional $w$NAF method for modular exponentiation -- the
classical method uses a digit set of the form $\{1,3,\dots,m\}$
which is extended here to any set of odd integers of the form
$\{1,d_2,\dots, d_n\}$. We give a formula for the average density of
non-zero terms in this new representation and discuss its asymptotic
behavior when those digits are randomly chosen from a given set. We
also propose a specific method for the precomputation phase of the
exponentiation algorithm.
↧