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.

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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 e = 37 and their public modulus M = pq = 527. Break the code: Find their secret decoding exponent d.

Mathematics
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Here's a worked example http://en.wikipedia.org/wiki/RSA_(cryptosystem)#A_worked_example
I still don't understand...
Your goal is to find the inverse of \(37\) in mod \(\phi(527)\)

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Other answers:

Solve \[37x \equiv 1 \pmod{\phi(527)}\]
What is \[ϕ\]?
not familiar with euler totient function ?
nope
For example, if your message is 2 then d is 2=mod((mod(2^37, 527))^(d) ,527) Here's why: Since c is your encrypted message c=2^37 mod 527 Then since your original message was "2" then the decrypted message is 2 = c^d mod 527 Combine both to get the 1st equation http://www.wolframalpha.com/input/?i=2%3Dmod%28%28mod%282%5E37%2C+527%29%29%5E%28y%29+%2C527%29

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