November 2012
Intermediate to advanced
1200 pages
78h 13m
English
Pramod Pandya, CSU Fullerton
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(pe)=pe−pe−1 if p is a prime
Examples:
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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 ...
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