# 1)(i) Given p=19, q=23, and e=11 what is the Public Key Pu(e,N)? (...

## Question

1)(i) Given p=19, q=23, and e=11 what is the Public Key Pu(e,N)?
(ii) For p=19, q=23, what is the value of φ?
(iii) Given the following expression for d=(φx+1)/e, what is the Private Key Pr(d,N)?
(iv) For a message M=14, what is the ciphertext C?
(v) For the ciphertext C=142, recover the original message M.

2) What is the number of 4-cycles (cycles of length 4) in a complete bipartite graph Km,n?

## Solution Preview

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1)i). N=p*q =23*19=437 => the public key Pu(e,N) = (11,437)
ii). φ=(p-1)(q-1)=(19-1)(23-1)=18*22=396...

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