# number theory – RSA Crypto reconstructing m by knowing (m mod p)

Let $$c = m^e mod N$$ be a RSA-ciphertext with $$N = pq$$.

Let
$$m_p = m mod p$$ be known

Knowing this, how can i reconstruct $$m$$ in polynomial time with respect to $$log N$$ and $$log e$$ ?

I suspect it might have to do with chinese remainder theorem, but i am not entirely sure. I know we need to find m, such that

$$gcd(m – m^e, N) = p$$, but i dont quite see, how we can do that in polynomial time