MHB What Are the Real-Life Applications of the Euler Totient Function?

Click For Summary
The Euler Totient Function, φ(n), is notably applied in RSA Public Key Encryption, which secures digital communications. Its significance lies in the property that a^φ(n) ≡ 1 (mod n), which is crucial for encryption and decryption processes. The discussion highlights the need for tangible methods to introduce the function, emphasizing its practical implications in cryptography. Overall, the Euler Totient Function plays a vital role in modern security systems, showcasing its real-life applications. Understanding its applications can enhance appreciation for its mathematical importance.
matqkks
Messages
280
Reaction score
5
What is most motivating and tangible way of introducing this function? Does it in itself have any real life applications that have an impact. I can only think of a^phi(n)=1 (mod n) which is powerful result but is this function used elsewhere.
 
Mathematics news on Phys.org
matqkks said:
What is most motivating and tangible way of introducing this function? Does it in itself have any real life applications that have an impact. I can only think of a^phi(n)=1 (mod n) which is powerful result but is this function used elsewhere.

One of the most remarkable application of the $\displaystyle \varphi(n)$ is the RSA Public Key Encryption...

RSA Encryption -- from Wolfram MathWorld

Kind regards

$\chi$ $\sigma$
 
Thread 'Erroneously finding discrepancy in transpose rule'

Thread 'Erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
View full post »

Similar threads

How Is the Euler Totient Function Applied in Real Life?
  • · Replies 3 ·
Replies
3
Views
3K
MHB What is the role of Euler's Totient function in Fermat's Little Theorem?
  • · Replies 6 ·
Replies
6
Views
4K
I Can Angular Velocity Accurately Control Ragdoll Limbs in Game Physics?
  • · Replies 6 ·
Replies
6
Views
3K
MHB Why Does Only n=4 Satisfy the Equation g(n)=n-2 in Euler's Totient Function?
  • · Replies 5 ·
Replies
5
Views
2K
MHB Elaborations about Euler's Totient Function
  • · Replies 8 ·
Replies
8
Views
3K
ArXiv:1301.7652 and Euler homogeneous function theorem
  • · Replies 6 ·
Replies
6
Views
2K
Continued Fractions: Motivation & Real Life Applications
  • · Replies 2 ·
Replies
2
Views
2K
MHB Real Life Applications of Ceiling and Floor Functions
  • · Replies 2 ·
Replies
2
Views
6K
I Alternating Harmonic Numbers are cool, spread the word!
  • · Replies 4 ·
Replies
4
Views
3K
I What are the resources for Pythagorean triples?
  • · Replies 10 ·
Replies
10
Views
2K