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Yes, it is possible. Like SEJPM suggested, you can use a variant of the Franklin-Reiter related-message attack to accomplish this. Let $\Delta = r_2 - r_1$. Compute $\gcd(X^{e} - c_e, (X + \Delta)^{s} - c_s)$ over $\mathbb{Z}/n\mathbb{Z}[X]$, which yields the linear polynomial $X - (m + r_1)$. Recovering $m$ is now trivial. This, of course, will only be ...


Intuitively, the reason fixed points are not a problem is the same reason that zeros in a one time pad are not. Because the transform is supposed to be random, a ciphertext that looks like plaintext could be that plaintext... or it could be any other plaintext. With proper encryption they are all equally likely. If I find out that the block that I ...

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