Number theory

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

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?

Play around with this "RSA calculator"

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