GATE Papers >> CSE >> 2017 >> Question No 44

Question No. 44 CSE | GATE 2017

In a RSA cryptosystem, a participant A uses two prime numbers p=13 and q=17 to genrate her public and private keys. If the public key of A is 35, then the privae key of A is __________.


Answer : 11.0 to 11.0


Solution of Question No 44 of GATE 2017 CSE Paper

$ \begin{array}{l}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;p=13,\;q=17\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;n=p\times q\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;=13\times17=221\\\;\;\;\;\;\;\;\;\;\;\mathrm\phi\left(n\right)=\left(p-1\right)\times\left(q-1\right)\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;=12\times16=192\\\left(d\times e\right)\;\mod\;\;\mathrm\phi\left(n\right)=1\\\left(d\times35\right)\;\mod\;192=1\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\mathit\;d=11\end{array} $

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