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Question: An RSA cipher has the public key pq=65 and e=7. What is the encrypted value of 3 integers a,b and c. $$ \begin{align*} &M={ C }^{ d }mod\quad pq,\quad M\quad <\quad pq,\quad and\quad \\ &C={ M }^{ e }\\ &by\quad substitution,\\ &{ C }^{ d }mod\quad pq\quad =\quad ({ M }^{ e }\quad mod\quad pq{ ) }^{ d }mod\quad pq \end{align*} $$

I have tried to research this question and found an overwhelming amount of information am not I am sure what my first steps should be, what the middle part is and how to end.

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  • $\begingroup$ any 3 integers x, where 0≤x≤9 $\endgroup$
    – user1787331
    Mar 17, 2016 at 15:52
  • $\begingroup$ I want to say yes, we do not need the sum of the digits encrypted. Just the separate integers. $\endgroup$
    – user1787331
    Mar 17, 2016 at 21:36

1 Answer 1

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$$ \begin{align*} &Assume\quad we\quad are\quad encrypting\quad 1\quad 2\quad 3\\ &C\quad =\quad Cyphertex,\quad M\quad =\quad Message\quad (plain\quad text)\\ &e\quad and\quad pq\quad =\quad public\quad key.\\ \\ &C\quad =\quad { M }^{ e }\quad mod\quad pq.\\ \\ &Let\quad pq\quad =\quad 65\\ &Let\quad e\quad =\quad 7\\ \\ &f(x)\quad =\quad { x }^{ 7 }\quad mod\quad 65\quad \\ \\ &f(1)\quad =\quad 1\\ &f(2)\quad =\quad 63\\ &f(3)\quad =\quad 42\\ \\ &123\quad \Rightarrow \quad RSA\quad 1\quad 63\quad 42 \end{align*} $$

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