i am trying to understand the differences of using k in the following scenarios to better understand the protocol and most importantly the consequences of using such k.
so i wonder, some user, call him A sends two messages to B using El gamal. some user C, is not happy he's not invited, so he listens and gets those two messages. he works really hard and gets the decryption of the first message sent. can he also the second in those cases:
first case: A sends two messages E(m) and E(2m), but uses a different random k each time. i think she should be worried, but the second message is still safe.
second case: A sends two messages E(m) and E(2m), but uses the same random k for both messages. however, C doesn't know that she didn't change this random value.
could you please elaborate on the safety regarding those two cases? i am pretty sure in the second case the message is not so confident and probably decrypted because he obtained a decryption of the first message, and same k was used twice, so he just needs to filter the message to make sense.
would really appreciate if you could give a mathematical explanation to help me understand the material better.