Anonymous
Anonymous asked in Computers & InternetSecurity · 8 years ago

# Need help with RSA Keys (Cryptography) Full question in Description?

Alice and Bob use RSA public-key cryptography. For his private key Bob chooses the prime numbers p=11 and q=17. For his public key he chooses the exponent e=23; Compute bobs private key and public key

Any help on how to go about working out this answer will be appreciated. Thank you

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• om
Lv 6
8 years ago

The Wikipedia page on the RSA algorithm (see the 'Sources' section below for a link) has a good step-by-step explanation of how the public and private keys are generated.

That page includes a worked example for p=61 and q=53. You should be able to use that as a template for your version with p=11 and q=17.

The only tricky part is finding d. That's where the Extended Euclidean Algorithm can be used. The good news is that with numbers this small, if you don't want to deal with that algorithm then it's perfectly reasonable to write a program that will calculate d by sheer brute force. Something like:

d = 1

while ( ( (d * e) % phi_n ) != 1 )

d = d + 1

print d

Of course as the numbers involved get bigger, this becomes increasingly less practical. At some point you'd want to switch to a better algorithm.

Source(s): Wikipedia's RSA Algorithm page: http://en.wikipedia.org/wiki/RSA_%28algorithm%29
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