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## Homework Statement

I'm trying to understand RSA and modular math better. I've studied some of the relations and rules, but I keep getting stuck when i try to follow an example all the way through. I'm also getting confused by how I'm supposed to treat ≡ vs = at some times. Here is the background in this particular example:

The encryption function is

**y ≡ x**, where x is the integer value of the plain text and y the integer value of the cipher text.

^{e}(mod n)I'm not sure if this means:

**y = x**, meaning y = the remainder of

^{e}(mod n)**x**or should i interpret it to mean:

^{e}/n**y (mod n) ≡ x**where i should solve for y, so that the remainder of

^{e}(mod n)**y/n**= the remainder of

**x**?

^{e}/nWould I do that using the Chinese remainder theorem or Euclid algorithm? or the relationship

**y = x**?

^{e}(mod n): ⇒ y-x/m = k## Homework Equations

In this example: e = 11, p = 13 , q = 29 and n = pq = 377. Φ(n) = (p-1)(q-1)= 336.

the values for the integer plain text is 110, 111, 119. Y is the cipher text.

**y ≡ 110**

y ≡ 111

y ≡ 119

^{11}≡ 310 (mod 377)y ≡ 111

^{11}≡ 132 (mod 377)y ≡ 119

^{11}≡ 189 (mod 377)What does y equal, and where did the numbers 310, 132, 189 (in red) come from??

According to the example the cipher text is 310, 132, 189.

**Here is a hyperlink to the entire example. http://math.gcsu.edu/%7Eryan/12capstone/papers/maxey.pdf [Broken]**

3. The Attempt at a Solution

3. The Attempt at a Solution

So now I'm confused. Considering the first line of the relevant equations...

Is it saying

**y = 110**, and

^{ 11}( mod 377) = 310**⇒ y ≡ 310 (mod 377) ⇒ y (mod 377) = 310 (mod 377)**?

if I calculate 110

^{ 11}(mod 377) does not equal 310 (mod 377)...

**110**

^{ 11}( mod 377) = 28531167061100000000000 (mod 377) = 372and

**310 (mod 377)**=

**310**.

So where does the number 310 come from??

According to the example y is the cipher text, and the cipher text is 310, so how do we find y.

Are we supposed to find y through the relationship..

**y ≡ 110**

y (mod 377)≡

^{11}(mod 377)y (mod 377)

**110**

^{11}(mod 377)Then we solve for y using anther method and come up with y = 310.

So, to recap...

1) Does

**y ≡ x**mean find y for

^{e}(mod n)**y (mod n) = x**In other words is the cipertext y, the remainder of

^{e}(mod n) ??**x**or is it a number that when divided by n has a remainder equal to the remainder of

^{e}(mod n)**x**divided by n.

^{e}2) Where did the red numbers (310, 132, and 189) come from in the example. Are these equal to the y's??

I would like to work through this by myself as much as possible, but I'm stuck and thoroughly confused.

Thanks for the help guys.

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