ABSTRACT
Several conventional encryption schemes were discussed in Chapter 9. The concept of public key was introduced in Section 9.3.4. In this chapter, we will discuss some public key encryption systems based onnumber theory. First, we give theminimal number theory and algebraic backgroundneeded to understand these schemes from a mathematical viewpoint (see Section 10.2). Then, we present, in Section 10.3, the most popular schemes based on number theory. We explain in Section 10.4 the computational number theory required to understand why these schemes run in (expected) polynomial time. To avoid overburdening the reader with number theory, we will postpone the number theory needed to understand the computational aspect until Section 10.4.We briefly discuss security issues in Section 10.7.
