Exponentiation Algorithms

Related Concepts

2^k-Ary Exponentiation; Binary Exponentiation Method; Fixed-Base Exponentiation; Fixed-Exponent Exponentiation; Sliding Window Exponentiation

Definition

Exponentiation is the repeated application of the group operation to a single group element.

Background

The problem of computing an exponentiation occurs frequently in modern cryptography, especially in public-key algorithms. Exponentiation is defined as the repeated application of the group operation to a single group element. If one assumes a multiplicative group, that is, the group operation is called “multiplication,” and one denotes the group element by g, an exponentiation can be written as

$$\underbrace{g \cdot g \cdot \ldots \cdot g }_{e\quad {times}} = {g}^{e}$$

This case is in particular relevant for RSA and discrete logarithm schemes in finite fields like the Diffie–Hellman key agreement. It should be kept in mind that the corresponding notation for additive groups, that is, groups where the group operation...