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How do you find RSA encryption key e?

es flag

How do you find RSA encryption key e when RSA modulus is n = 55 = 5 x 11 and your decryption is d = 37? Is this possible for large values of n say of the order of 1024 bits?

fgrieu avatar
ng flag
Hint: what's the sufficient condition you where told that makes $d$ valid w.r.t $n$ and $e$? (I can't tell, because not all teachers give the same one). Find $e$ satisfying this condition.
ming alex avatar
in flag
Do you mean that d is the decryption key? If so, you can calculate any decryption key $d$ or encryption key $e$ easily with **Extended Euclid Thoerm** by knowing $p$ and $q$. That is because of $e*d=1mod\varphi(n)$ where $\varphi(n)=\varphi(p)*\varphi(q)$.
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