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* PUSH NOTE : 09. Transport Layer Security.md

* PUSH ATTACHMENT : is-09-tls-handshake.png

* PUSH NOTE : 08. Public Key Infrastructure.md

* PUSH ATTACHMENT : is-08-certificate-validation.png

* PUSH NOTE : 07. Public Key Cryptography.md

* PUSH NOTE : 06. RSA and ElGamal Encryption.md

* PUSH NOTE : 05. Modular Arithmetic (2).md

* PUSH NOTE : 04. Modular Arithmetic (1).md

* PUSH NOTE : 03. Symmetric Key Cryptography (2).md

* PUSH ATTACHMENT : is-03-feistel-function.png

* PUSH ATTACHMENT : is-03-ecb-encryption.png

* PUSH ATTACHMENT : is-03-cbc-encryption.png

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* PUSH ATTACHMENT : is-03-ofb-encryption.png

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* PUSH NOTE : 02. Symmetric Key Cryptography (1).md

* PUSH NOTE : 01. Security Introduction.md

* PUSH ATTACHMENT : is-01-cryptosystem.png

* PUSH NOTE : 9. Public Key Encryption.md

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* PUSH NOTE : 7. Key Exchange.md

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* PUSH ATTACHMENT : mc-07-merkle-puzzles.png

* PUSH NOTE : 6. Hash Functions.md

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* PUSH ATTACHMENT : mc-06-davies-meyer.png

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* PUSH NOTE : 5. CCA-Security and Authenticated Encryption.md

* PUSH ATTACHMENT : mc-05-ci.png

* PUSH ATTACHMENT : mc-05-etm-mte.png

* PUSH NOTE : 4. Message Authentication Codes.md

* PUSH ATTACHMENT : mc-04-mac.png

* PUSH ATTACHMENT : mc-04-mac-security.png

* PUSH ATTACHMENT : mc-04-cbc-mac.png

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* PUSH NOTE : 2. PRFs, PRPs and Block Ciphers.md

* PUSH ATTACHMENT : mc-02-block-cipher.png

* PUSH ATTACHMENT : mc-02-feistel-network.png

* PUSH ATTACHMENT : mc-02-des-round.png

* PUSH ATTACHMENT : mc-02-DES.png

* PUSH ATTACHMENT : mc-02-aes-128.png

* PUSH ATTACHMENT : mc-02-2des-mitm.png

* PUSH NOTE : 16. The GMW Protocol.md

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* PUSH NOTE : 13. Sigma Protocols.md

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* PUSH ATTACHMENT : mc-10-schnorr-identification.png

* PUSH ATTACHMENT : mc-13-okamoto.png

* PUSH ATTACHMENT : mc-13-chaum-pedersen.png

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* PUSH NOTE : 12. Zero-Knowledge Proofs (Introduction).md

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* PUSH NOTE : 10. Digital Signatures.md

* PUSH ATTACHMENT : mc-10-dsig-security.png

* PUSH NOTE : 1. OTP, Stream Ciphers and PRGs.md

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* DELETE FILE : _posts/Lecture Notes/Internet Security/2023-09-10-security-intro.md

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Sungchan Yi
2024-11-12 20:54:38 +09:00
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_posts/lecture-notes/modern-cryptography/2023-09-21-macs.md
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@@ -14,9 +14,9 @@ title: 4. Message Authentication Codes
date: 2023-09-21
github_title: 2023-09-21-macs
image:
path: assets/img/posts/Lecture Notes/Modern Cryptography/mc-04-mac-security.png
path: assets/img/posts/lecture-notes/modern-cryptography/mc-04-mac-security.png
attachment:
folder: assets/img/posts/Lecture Notes/Modern Cryptography
folder: assets/img/posts/lecture-notes/modern-cryptography
---
Message authentication codes (MAC) were designed to provide message integrity. Bob receives a message from Alice and wants to know if this message was not modified during transmission. For MACs, the message itself does not have to be secret. For example, when we download a file the file itself does not have to be protected, but we need a way to verify that the file was not modified.
@@ -27,7 +27,7 @@ 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-notes/modern-cryptography/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**.
>
@@ -59,7 +59,7 @@ 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-notes/modern-cryptography/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.
>
@@ -124,7 +124,7 @@ 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-notes/modern-cryptography/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 $F_k := F(k, \cdot)$.
>
@@ -212,7 +212,7 @@ 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-notes/modern-cryptography/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.
>