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Issues in RSA setup

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Suppose we have public key: $$n= 1015, e= 3$$ and private key: $$d= 635, p= 35, q= 29, \phi(n)= 952$$ For $m = 100$, we have $$c = m^e ~mod~n = 100^3 mod~1015 = 225.$$ To decipher this, let us take $$c^d~mod~n$$ which is $$225^{635}~mod~1015$$ which equals $$680$$ But $680 \neq 100$ so this means that RSA incorrectly decrypted it right? Why does this happen?

Asked By : Ragnar
Answered By : D.W.

Your public key is not a legal RSA public key. In RSA, $n$ must be a product of two primes, but 35 is not a prime. Therefore, things don't work right: for instance, you got the wrong value of $\phi(n)$.

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