# RSA calculate public exponent

Suppose I have two messages $$m_1$$ and $$m_2$$ as well as $$c_1$$ and $$n$$. It's standard RSA so $$c_1 = m_1^e \ mod \ n$$, $$c_2 = m_2^e \ mod \ n$$. Further assume the only information we have about e is that it is smaller than $$2^{2048}$$. Is there a way to find it? (According to this it is not)

• Is there some reason why you think the answers to that duplicate you linked to would be wrong? – Ilmari Karonen Apr 22 '19 at 21:11
• no particular one, I just couldn't wrap my head around it for some reason. – S. L. Apr 23 '19 at 9:34

If it were, then RSA would be insecure; the same way to recover $$e$$ from $$m_1, m_1^e \bmod n$$ would be able to recover the private key $$d$$ from $$c_1, c_1^d \bmod n$$ (as that's the same problem, only using different symbols).