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fix: broken image links have been fixed

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Sungchan Yi
2024-02-09 14:25:14 +09:00
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_posts/Lecture Notes/Modern Cryptography/2023-09-21-macs.md
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@@ -26,7 +26,7 @@ On the other hand, MAC fixes data that is tampered in purpose. We will also requ
## Message Authentication Code
![mc-04-mac.png](../../../assets/img/posts/Lecture%20Notes/Modern%20Cryptography/mc-04-mac.png)
![mc-04-mac.png](/assets/img/posts/Lecture%20Notes/Modern%20Cryptography/mc-04-mac.png)
> **Definition.** A **MAC** system $\Pi = (S, V)$ defined over $(\mathcal{K}, \mathcal{M}, \mathcal{T})$ is a pair of efficient algorithms $S$ and $V$ where $S$ is a **signing algorithm** and $V$ is a **verification algorithm**.
>
@@ -58,7 +58,7 @@ In the security definition of MACs, we allow the attacker to request tags for ar
For strong MACs, the attacker only has to change the tag for the attack to succeed.
![mc-04-mac-security.png](../../../assets/img/posts/Lecture%20Notes/Modern%20Cryptography/mc-04-mac-security.png)
![mc-04-mac-security.png](/assets/img/posts/Lecture%20Notes/Modern%20Cryptography/mc-04-mac-security.png)
> **Definition.** Let $\Pi = (S, V)$ be a MAC system defined over $(\mathcal{K}, \mathcal{M}, \mathcal{T})$. Given an adversary $\mathcal{A}$, the security game goes as follows.
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@@ -123,7 +123,7 @@ The above construction uses a PRF, so it is restricted to messages of fixed size
### CBC-MAC
![mc-04-cbc-mac.png](../../../assets/img/posts/Lecture%20Notes/Modern%20Cryptography/mc-04-cbc-mac.png)
![mc-04-cbc-mac.png](/assets/img/posts/Lecture%20Notes/Modern%20Cryptography/mc-04-cbc-mac.png)
> **Definition.** For any message $m = (m_0, m_1, \dots, m_{l-1}) \in \left\lbrace 0, 1 \right\rbrace^{nl}$, let $F_k := F(k, \cdot)$.
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@@ -211,7 +211,7 @@ Since CBC-MAC is vulnerable to extension attacks, we encrypt the last block agai
ECBC-MAC doesn't require us to know the message length in advance, but it is relatively expensive in practice, since a block cipher has to be initialized with a new key.
![mc-04-ecbc-mac.png](../../../assets/img/posts/Lecture%20Notes/Modern%20Cryptography/mc-04-ecbc-mac.png)
![mc-04-ecbc-mac.png](/assets/img/posts/Lecture%20Notes/Modern%20Cryptography/mc-04-ecbc-mac.png)
> **Theorem.** Let $F : \mathcal{K} \times X \rightarrow X$ be a secure PRF. Then for any $l \geq 0$, $F_\mathrm{ECBC} : \mathcal{K}^2 \times X^{\leq l} \rightarrow X$ is a secure PRF.
>