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3. (10 points) You see that someone’s RSA public key is (23,56153). You figure out how...

3. (10 points) You see that someone’s RSA public key is (23,56153). You figure out how to factor 56153 into 233 and 241. Knowing this, tell me what that person’s public key is (if it actually exists). If there exists no valid private RSA key for this, then justify why that is the case.

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Answer #1

Given public key

e=23

n=56153

Valid public key GCD(phy(n),e)=1

n=56153=233*241

Phi(n)=232*240=55680

gcd(23,56153)=1 so public key e is valid

Private key (d)

d*e mod phi(n)=1

23*d mod 55680=1

d=19367

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