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The House of Lilliput is using RSA encryption to receive secret messages from all the realms. They have published their public encoding exponent 37 and their public modulus M=pq=527.

Break the code: Find their secret decoding exponent d

MIRB16  Jun 21, 2018
 #1
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Hey Guest

 

We first need to factor the public modulus \(M = pq = 527 \Rightarrow 527 = 17 \cdot 31. \)

 

Therefore \(p =17 \ \&\ q=31 \)

 

The definition of a secret decryption exponent is the multiplicative inverse of the public encoding exponent, in modulo \( (p-1)(q-1)\).

 

Therefore \(d= 37^{-1} \pmod{480}. \Rightarrow d=\boxed{13}\)

 

I hope this helped,

 

Gavin

GYanggg  Jun 21, 2018
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Thank you so much!! That really helped!

MIRB16  Jun 22, 2018
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Gavin It would help more if you would show how to do this.

This isn’t the right answer.

When I type input 37^-1 mod 480 into the calculator I get 0.027027027

Guest Jun 21, 2018
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Go online to this page which gives a detailed numerical example on how to break the RSA encryption.

Look under: A working example:

https://simple.wikipedia.org/wiki/RSA_algorithm

Guest Jun 21, 2018
 #4
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Thanks. This shows how to encrypt and decrypt but not how to “crack” the key.

Do you know of a website where it shows the steps on how to do this?

Guest Jun 21, 2018
 #5
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Play around with this "RSA calculator"

 

https://www.cs.drexel.edu/~jpopyack/IntroCS/HW/RSAWorksheet.html

Guest Jun 21, 2018

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