RSA padding: risk of using constants Assume I want to make my RSA secure because I heard that textbook RSA, especially in conjunction with low exponents, is very risky. I decide to limit my message length to 100 and subsequently construct my padded message as follows:

m = '\x01'*70 + m + '\x01'*70


To improve performance, I choose $e=3$.

Why is this risky? After all, the padded message is large enough, i.e. knowing that $c=m^3 + k*n$, $k$ will be too high to bruteforce. At first glance I don't see any attacks that could work here therefore it should be safe?
By narrowing the space of messages and ciphertexts you are willing to consider to a tiny fraction of fewer than $1/2^{1000}$ of them, you cannot prove that an algorithm for breaking this translates to an algorithm for computing cube roots modulo $n$ in general.

Consequently you can't rely on the decades of work that have been put into failing to find a way to compute cube roots modulo $n$, and you have to redo those decades of failure anew in order to get confidence in the system's security.