New answers tagged nonce
1
In ElGamal encryption like you said for unknown $m_1$ and known $m_2$ we have:
$m_1: C_1=g^k\ mod\ p,\ D_1=m_1.g^{a.k}$
$m_2: C_2=g^k\ mod\ p,\ D_2=m_2.g^{a.k}$
$k$ is the same in both encryptions, by dividing $D_1$ and $D_2$ we have:
${D_1\over D_2}={m_1\over m_2} => D_1.m_2 = D_2.m_1$
$m_2$ , $D_1$ and $D_2$ and are known so now we can calculate $...
1
A nonce on its own does not prevent replay attacks. It is just a number, it doesn't do anything, it can't give any guarantees. You could define a protocol with a nonce, that has no cryptographic functions at all - and it's fairly obvious, that is not secure in any sense.
It all comes down to how you use the nonce in a protocol and what kind of security ...
5
Given no knowledge of the MAC key and that M1 != M2, it is not possible to compute MAC(K, M2) from MAC(K, M1).
More generally, it isn't possible to determine the MAC of any message you haven't already seen. (Again, without the key.) The definition of a nonce is a number which is only used once with a given key.
Bob ensures that nonces are only used once ...
0
Messages 4 and 5 are meant to protect the recipient B from a replay attack. It is a basic challenge response mechanism. Otherwise an attacker could just replay previous messages and have the very same interaction with B again. That is bad, if e.g. the message is just "increase some counter", or another message that has a lasting effect or changes a state.
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