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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

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

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

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

* 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

* PUSH ATTACHMENT : mc-09-ss-pke.png

* PUSH NOTE : 7. Key Exchange.md

* PUSH ATTACHMENT : mc-07-dhke.png

* PUSH ATTACHMENT : mc-07-dhke-mitm.png

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

* PUSH NOTE : 6. Hash Functions.md

* PUSH ATTACHMENT : mc-06-merkle-damgard.png

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

* PUSH ATTACHMENT : mc-06-hmac.png

* 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

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

* 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

* PUSH ATTACHMENT : mc-16-beaver-triple.png

* PUSH NOTE : 13. Sigma Protocols.md

* PUSH ATTACHMENT : mc-13-sigma-protocol.png

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

* PUSH ATTACHMENT : mc-13-okamoto.png

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

* PUSH ATTACHMENT : mc-13-gq-protocol.png

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

* PUSH ATTACHMENT : mc-12-id-protocol.png

* PUSH NOTE : 10. Digital Signatures.md

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

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

* PUSH ATTACHMENT : mc-01-prg-game.png

* PUSH ATTACHMENT : mc-01-ss.png

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

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* DELETE FILE : _posts/Lecture Notes/Internet Security/2023-09-25-modular-arithmetic-1.md

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* DELETE FILE : _posts/Lecture Notes/Internet Security/2023-10-04-rsa-elgamal.md

* DELETE FILE : _posts/Lecture Notes/Internet Security/2023-10-09-public-key-cryptography.md

* DELETE FILE : _posts/Lecture Notes/Internet Security/2023-10-16-pki.md

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Sungchan Yi
2024-11-12 20:54:38 +09:00
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_posts/lecture-notes/modern-cryptography/2023-10-03-key-exchange.md
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@@ -14,9 +14,9 @@ title: 7. Key Exchange
date: 2023-10-03
github_title: 2023-10-03-key-exchange
image:
path: assets/img/posts/Lecture Notes/Modern Cryptography/mc-07-dhke.png
path: assets/img/posts/lecture-notes/modern-cryptography/mc-07-dhke.png
attachment:
folder: assets/img/posts/Lecture Notes/Modern Cryptography
folder: assets/img/posts/lecture-notes/modern-cryptography
---
In symmetric key encryption, we assumed that the two parties already share the same key. We will see how this can be done.
@@ -75,7 +75,7 @@ $$
We assume that the description of $p$, $q$ and $g$ are generated at the setup and shared by all parties. Now the actual protocol goes like this.
![mc-07-dhke.png](../../../assets/img/posts/Lecture%20Notes/Modern%20Cryptography/mc-07-dhke.png)
![mc-07-dhke.png](../../../assets/img/posts/lecture-notes/modern-cryptography/mc-07-dhke.png)
> 1. Alice chooses $\alpha \leftarrow \mathbb{Z}_q$ and computes $g^\alpha$.
> 2. Bob chooses $\beta \leftarrow \mathbb{Z}_q$ and computes $g^\beta$.
@@ -190,7 +190,7 @@ Taking $\mathcal{O}(N)$ steps is impractical in the real world, due to many comm
We assumed that the adversary only eavesdrops, but if the adversary carries out active attacks, then DHKE is not enough. The major problem is the lack of **authentication**. Alice and Bob are exchanging keys, but they both cannot be sure that there are in fact communicating with the other. An attacker can intercept messages and impersonate Alice or Bob. This attack is called a **man in the middle attack**, and this attack works on any key exchange protocol that lacks authentication.
![mc-07-dhke-mitm.png](../../../assets/img/posts/Lecture%20Notes/Modern%20Cryptography/mc-07-dhke-mitm.png)
![mc-07-dhke-mitm.png](../../../assets/img/posts/lecture-notes/modern-cryptography/mc-07-dhke-mitm.png)
The adversary will impersonate Bob when communicating with Alice, and will do the same for Bob by pretending to be Alice. The values of $\alpha, \beta$ that Alice and Bob chose are not leaked, but the adversary can decrypt anything in the middle and obtain the plaintext.
@@ -212,7 +212,7 @@ Before Diffie-Hellman, Merkle proposed an idea for secure key exchange protocol
The idea was to use *puzzles*, which are problems that can be solved with some effort.
![mc-07-merkle-puzzles.png](../../../assets/img/posts/Lecture%20Notes/Modern%20Cryptography/mc-07-merkle-puzzles.png)
![mc-07-merkle-puzzles.png](../../../assets/img/posts/lecture-notes/modern-cryptography/mc-07-merkle-puzzles.png)
> Let $\mathcal{E} = (E, D)$ be a block cipher defined over $(\mathcal{K}, \mathcal{M})$.
> 1. Alice chooses random pairs $(k_i, s_i) \leftarrow \mathcal{K} \times \mathcal{M}$ for $i = 1, \dots, L$.