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

Break the code: Find their secret decoding exponent d.

Question

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

ganeshie8 · Answer

Our goal here in breaking the code is to  find "x" that satisfies : 

$$x^{37}\equiv c \pmod{527}$$

where $c$ the encrypted message

ganeshie8 · Answer

Recall euler's extension to little fermat : 
$$a^{\phi(n)}\equiv 1\pmod{n}$$

claire.bracken · Answer

yup @ganeshie8