Computer and Information Security Handbook, 2nd Edition

Chapter 70

Advanced Data Encryption

Pramod Pandya,    CSU Fullerton

1 Mathematical Concepts Reviewed

In this section we introduce the necessary mathematics of cryptography: Integer and Modular Arithmetic, Fermat’s Theorem [1]:

Euler’s Phi-Function ϕ(n)

Euler’s totient function finds the number of integers that are both smaller than n and coprime to n:

1. ϕ(1)=0

2. ϕ(p)=p–1 if p is a prime

3. ϕ(m×n)=ϕ(n)×ϕ(m) if m, and n are coprime

4. ϕ(p^e)=p^e−p^e−1 if p is a prime

Examples:

Fermat’s Little Theorem

In the 1970s, the creators of digital signatures and public-key cryptography realized that the framework for their research was already laid out in the ...