Rsa

[RK4]

Hi all! I'm working on the following problem:

 

If the ciphertext message produced by RSA encryption with the key (e, n) = (5, 2881) is 0504 1874 0347 0515 2088 2356 0736 0468, what is the plaintext message?

 

My work thus far:

 

2881 = 43 * 67

 

phi(2881) = phi(43 * 67) = phi(43) * phi(67) = 42 * 66 = 2772

 

From here I need to find an inverse of 5 modulo 2772 which is 1109 and then raise each ciphertext block to power 1109 mod 2881 to retrieve the plaintext message.

 

I don't know how to do this last step...

 

0504^1109 = ____ (mod 2881)

 

How to fill in this blank above?

 

Please advise. Thanks!

[Dave]

Use Mathematica. It'll work out the answer extremely quickly. (I can't think about a mathematical way of doing it atm).

 

I get an answer of 400 precisely.

[RK4]

Use Mathematica. It'll work out the answer extremely quickly. (I can't think about a mathematical way of doing it atm).

 

I get an answer of 400 precisely.

 

What's the command you're using in Mathematica?

 

Can you give me an example here..

 

A sample run perhaps...

 

Thanks!

[Dave]

Just use the "Mod" function. For example, the command I used to calculate this was:

 

Mod[504^1109, 2881]

[RK4]

Just use the "Mod" function. For example' date=' the command I used to calculate this was:

 

Mod[504^1109, 2881']

 

Thanks a bunch!

[Dave]

Not a problem