Suppose we have $(n,e)$ and the ciphertext $c$ where the public exponent $e$ is of the same length, 1023-bit, as the modulus $n$. It is also assumed that the factors of $n$ are balanced. The message is decrypted using CRT with small exponents but unknown to us, attacker. Is it possible to decrypt $c$ in such a scenario?
I have checked the Wiener's attack on https://en.wikipedia.org/wiki/Wiener%27s_attack but the example requires those parameters that are not available to us in this situation.