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1

It is not secure. Suppose an attacker Mallory has oracle access to the encryption device of Alice. Mallory is able to get Alice to encrypt any chosen plain text, but Mallory is not able to decrypt any cipher text that is not chosen by Mallory. A typical, practical, scenario could be that Mallory controls javascript that is executed by Alice's web browser, ...


3

No, it is not necessarily secure. Here is a simplified example of why not. Assume one block zero messages are encrypted without padding. The ciphertext is $I||E(I \oplus 0)$. The MAC value is thus $E(E(I) \oplus E(I)) = E(0)$. So regardless of the IV, the MAC is the same for all such messages. So if you encrypt several zero messages you can leak that fact ...


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Now the standard key size for RSA is recommended of 2048 bits. This is large enough to never having a collision in practice, where brute force is 2^{2048}. Even if we consider some attacks that allow to break it with half the key size or in birthday attack, this number is quite secure. However, larger the key size, more overhead and lower efficiency.


1

This depends on the MAC because there are different kinds of attacks to consider. If the best attack is randomly trying authentication tags, then the key does not matter. If the best attack is brute forcing the key, then key renewal does mean that the attacker has to "start anew", but as long as the key space is large enough that the probability of finding ...


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I just came across this question and was surprised that no one referenced the paper: A Natural Language Approach to Automated Cryptanalysis of Two-time Pads by Mason et al. at ACM CCS 2006. This shows how to solve this problem in an automated and intelligent way.


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If you reuse a nonce, you lose confidentiality for the messages with that nonce. Messages with other nonces retain their confidentiality. However, the attacker can also attack the MAC part (Poly1305) and generate a third and more messages with the same nonce. See: Why is Poly1305 popular given its 'sudden death' properties? So unless you have a way ...



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