Abstract
Online visualization systems have come to be heavily used in education, particularly for online learning. Most e-learning systems, including interactive learning systems, have been designed to simplify understanding the ideas of some main problems or in general overall course materials. This paper presents a novel interactive visualization system for one of the most important operation in public-key cryptosystems. This operation is modular exponentiation using addition chains. An addition chain for a natural number e is a sequence 1 = a(0) < a(1) < ... < a(r) = e of numbers such that for each 0 < i <= r, a(i) = a(j) + a(k) for some 0 <= k <= j < i. Finding an addition chain with minimal length is NP-hard problem. The proposed system visualizes how to generate addition chains with minimal length using depth-first branch and bound technique and how to compute the Modular exponentiation using addition chains.