4
if there's an inner-layer error correcting code, will it be able to work without an encryption algorithm based on a stream cipher?
Depends on how the inner error correcting code works; what you want is an encryption method that does not radically increase the 'size' of any ciphertext errors (where 'size' is what's relevant to the error correcting code), ...
3
If the MAC is theoretically secure, but its implementation has a side channel (like by Differential Power Analysis, maybe even timing) leaking information about the MACed message (but not the key), and the encryption is secure including it's implementation, then neither MtE nor MtEtM are safe (because the side channel leaks about the message), but EtM is ...
2
So if Alice wants to send a message to Bob, a pair of public and private key is generated. But if Bob wants to send something back to Alice, must another pair of public and private key be generated?
Yes. Bob's public/private key pair, which protected the Alice-to-Bob transfer, is not usable to send data to Alice. However it's usable by anyone [assumed ...
1
Real encryption algorithms (not the sort of thing you're mentioning) like AES and ChaCha20 have their speeds measured in "cycles per byte". That is, how many CPU clock cycles does it take to encrypt one byte of data.
The speed will differ a bit depending on the CPU architecture used (eg AES often has hardware acceleration instructions built into ...
1
In general this is a moot point, as modern encryption schemes are designed so that the recipient knows if they have used the correct key or not. It is an interesting question to ask about encryption primitives, like a block cipher. Put more precisely, you are asking whether there is always a $k_3$ such that
$D_{k_2}(E_{k_1}) = E_{k_3}$
This is essentially ...
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