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feat: internet security midterm notes (#128)
* [PUBLISHER] upload files #114 * [PUBLISHER] upload files #115 * PUSH NOTE : 1. OTP, Stream Ciphers and PRGs.md * PUSH ATTACHMENT : mc-01-prg-game.png * PUSH ATTACHMENT : mc-01-ss.png * [PUBLISHER] upload files #116 * 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 * [PUBLISHER] upload files #117 * PUSH NOTE : 01. Security Introduction.md * PUSH ATTACHMENT : is-01-cryptosystem.png * [PUBLISHER] upload files #118 * [PUBLISHER] upload files #119 * [PUBLISHER] upload files #120 * [PUBLISHER] upload files #121 * [PUBLISHER] upload files #122 * [PUBLISHER] upload files #123 * PUSH NOTE : 07. Public Key Cryptography.md (#124) * fix: links fixed * [PUBLISHER] upload files #125 * PUSH NOTE : 08. Public Key Infrastructure.md * PUSH ATTACHMENT : is-08-certificate-validation.png * [PUBLISHER] upload files #126 * PUSH NOTE : 09. Transport Layer Security.md * PUSH ATTACHMENT : is-09-tls-handshake.png * [PUBLISHER] upload files #127 * PUSH NOTE : 08. Public Key Infrastructure.md * PUSH ATTACHMENT : is-08-certificate-validation.png * fix: fixed internal, external links
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@@ -171,6 +171,8 @@ Since the adversary can see the ciphertext, this kind of relation leaks some inf
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Also, the key is (at least) as long as the message. This is why OTP is rarely used today. When sending a long message, two parties must communicate a very long key that is as long as the message, *every single time*! This makes it hard to manage the key.
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## Shannon's Theorem
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So is there a way to reduce the key size without losing perfect secrecy? Sadly, no. In fact, the key space must be as least as large as the message space. This is a requirement for perfectly secret schemes.
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> **Theorem**. If $(G, E, D)$ is a perfectly secret encryption scheme, then $\lvert \mathcal{K} \rvert \geq \lvert \mathcal{M} \rvert$.
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@@ -290,7 +292,7 @@ We can deduce that if a PRG is predictable, then it is insecure.
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*Proof*. Let $\mathcal{A}$ be an efficient adversary (next bit predictor) that predicts $G$. Suppose that $i$ is the index chosen by $\mathcal{A}$. With $\mathcal{A}$, we construct a statistical test $\mathcal{B}$ such that $\mathrm{Adv}_\mathrm{PRG}[\mathcal{B}, G]$ is non-negligible.
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1. The challenger PRG will send a bit string $x$ to $\mathcal{B}$.
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- In experiment $0$, PRG gives pseudorandom string $G(k)$.
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@@ -316,7 +318,7 @@ The theorem implies that if next bit predictors cannot distinguish $G$ from true
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To motivate the definition of semantic security, we consider a **security game framework** (attack game) between a **challenger** (ex. the creator of some cryptographic scheme) and an **adversary** $\mathcal{A}$ (ex. attacker of the scheme).
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> **Definition.** Let $\mathcal{E} = (G, E, D)$ be a cipher defined over $(\mathcal{K}, \mathcal{M}, \mathcal{C})$. For a given adversary $\mathcal{A}$, we define two experiments $0$ and $1$. For $b \in \lbrace 0, 1 \rbrace$, define experiment $b$ as follows:
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>
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