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How to break RSA when $q = e^{-1} \bmod p$?

Note that $q = e^{-1}\bmod p$ means there exists an integer $k$ such that $qe = 1 + kp$. Hence $$ne = pqe = p\cdot(1+kp)/e\cdot e = p + kp^2 \,\text. \label{n-eq}\tag{$\ast$}$$ From $qe=1+kp$, we ...
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Encrypting two messages with the same content with different keys/IVs still secure if attacker knows they are the same?

Yes, that should be secure as long as each algorithm is CPA-secure (as AES, Chacha20 and Serpent should be), and the keys are chosen independently and uniformly at random (different keys is not enough)...
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Key Committing AES-GCM

do I understand correctly that $\mathcal{A}$ needs to be able to 'modify' the ciphertext $C$ to be able to perform the outlined attacks? No, these attacks assume that the attacker generates $C$; he ...
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