4
You'll have to guess the plaintext of at least one block (128 bits) that is on a 128 bit boundary from the start of the GCM ciphertext. Then you can XOR it to retrieve 128 bits of the key stream.
Now the key stream you can decrypt since you have the key. This will get you a counter value. The counter in GCM mode starts with a 12 byte nonce and the counter ...
3
How is asymmetric cryptography safe under these conditions?
Well, you sort of outlined (but see kelalaka's corrections) how you would use asymmetric crypto to do authentication; that is, to make sure that the message was actually sent from $A$.
You ask "how does that provide privacy?". The answer, of course, is "if that's all you do, it doesn't".
If we ...
1
Why do we choose the value of e such that e is relatively prime to the totient (as opposed to just being relatively prime to n?)
The final goal of RSA encryption is to have $m = c^d \bmod n$, which is the same as $m = (m^e)^d \bmod n \rightarrow m = m^{ed} \bmod n$, i.e., if you encrypt and then decrypt, you get the same original message. For that last ...
1
Firstly, you misunderstood what is a signature and encryption with the public key.
A signature requires a hash then sign paradigm with the senders private key so that any receiver can verify the signature. The RSA paper gave the first idea to digital signatures that were insecure and the Rabin Signature released in 1979 is the fist secure signature that ...
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