I How Does the Equation D x E mod Φ(N) = 1 Relate to RSA Encryption?

  • I
  • Thread starter Thread starter brajesh
  • Start date Start date
  • Tags Tags
    Mathematics
AI Thread Summary
RSA encryption relies on the relationship between the encoding key (E), decoding key (D), and the totient function (Φ(N)). The equation D x E mod Φ(N) = 1 indicates that D and E are multiplicative inverses modulo Φ(N), which is crucial for the encryption and decryption process. Understanding this relationship helps in determining D once E is chosen, ensuring that the decryption process correctly retrieves the original plaintext message (M) from the encrypted message (C). The discussion highlights the importance of the totient function in RSA and suggests that additional resources, like Wikipedia and online calculators, can aid in grasping these concepts. Mastery of these equations is essential for a complete understanding of RSA encryption.
brajesh
Messages
62
Reaction score
15
TL;DR Summary
Understanding the RSA mathematics
Please help me understand the RSA encryption.
I understand part of it, then I don't understand.

Definitions:

M=plain text message
C=encrypted message
N=public key
E=encoding key
D=decoding key
P,Q are prime factors on N

I get that
P x Q = N (where P and Q are primes).

I get that

Φ(N) = (P-1) x (Q-1)

I get that

MEmodN = C

I get that

CDmodN = M

But after this I don't understand the relevance of this equation to solve D and E

D x E mod Φ(N) = 1

Seems to be some step or something obvious I'm missing?
 
Mathematics news on Phys.org
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Thread 'Video on imaginary numbers and some queries'
Hi, I was watching the following video. I found some points confusing. Could you please help me to understand the gaps? Thanks, in advance! Question 1: Around 4:22, the video says the following. So for those mathematicians, negative numbers didn't exist. You could subtract, that is find the difference between two positive quantities, but you couldn't have a negative answer or negative coefficients. Mathematicians were so averse to negative numbers that there was no single quadratic...
Thread 'Unit Circle Double Angle Derivations'
Here I made a terrible mistake of assuming this to be an equilateral triangle and set 2sinx=1 => x=pi/6. Although this did derive the double angle formulas it also led into a terrible mess trying to find all the combinations of sides. I must have been tired and just assumed 6x=180 and 2sinx=1. By that time, I was so mindset that I nearly scolded a person for even saying 90-x. I wonder if this is a case of biased observation that seeks to dis credit me like Jesus of Nazareth since in reality...

Similar threads

Replies
7
Views
2K
Replies
2
Views
1K
Replies
3
Views
3K
Replies
1
Views
920
Replies
3
Views
1K
Replies
3
Views
2K
Back
Top