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**+2 **

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

#2**0 **

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

#3**0 **

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