+753 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
+983 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
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
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
