408 lines
17 KiB
HTML
408 lines
17 KiB
HTML
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<body class="markdown-body">
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<h2>
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<a href="index.html"><code>~</code></a>
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</h2>
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<div class="markdown-heading">
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<h1 class="heading-element">Real World Crypto 101</h1>
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<a
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id="user-content-real-world-crypto-101"
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class="anchor"
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aria-label="Permalink: Real World Crypto 101"
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href="#real-world-crypto-101"
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><span aria-hidden="true" class="octicon octicon-link"></span
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></a>
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</div>
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<p>
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My notes when reading
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<a
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href="https://www.manning.com/books/real-world-cryptography"
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rel="nofollow"
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>Real-World Cryptography</a
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>
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</p>
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<div class="markdown-heading">
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<h2 class="heading-element"><strong>Hash</strong> function</h2>
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<a
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id="user-content-hash-function"
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class="anchor"
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aria-label="Permalink: Hash function"
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href="#hash-function"
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><span aria-hidden="true" class="octicon octicon-link"></span
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></a>
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</div>
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<p>... convert from input to digest</p>
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<ul>
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<li>Pre-image resistance: Given digest, can not find input</li>
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<li>
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Second pre-image resistance: Given input, digest, can not find another
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input produce same digest. Small change to input make digest big change.
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</li>
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<li>Collision resistance: Can not find 2 input produce same digest.</li>
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</ul>
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<div class="markdown-heading">
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<h2 class="heading-element">
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<strong>MAC</strong> aka Message Authentication Code
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</h2>
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<a
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id="user-content-mac-aka-message-authentication-code"
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class="anchor"
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aria-label="Permalink: MAC aka Message Authentication Code"
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href="#mac-aka-message-authentication-code"
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><span aria-hidden="true" class="octicon octicon-link"></span
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></a>
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</div>
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<p>... produce from key, message to authentication tag.</p>
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<ul>
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<li>A send B message with MAC (generate from message and A key).</li>
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<li>
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B double check message with MAC (generate from receive message and B
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key).
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</li>
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<li>A and B use same key.</li>
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</ul>
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<div class="highlight highlight-source-mermaid">
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<pre><span class="pl-k">sequenceDiagram</span>
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<span class="pl-k">participant</span> <span class="pl-ent">alice</span>
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<span class="pl-k">participant</span> <span class="pl-ent">bob</span>
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<span class="pl-ent">alice </span><span class="pl-k">->></span> <span class="pl-ent">bob</span><span class="pl-k">:</span> <span class="pl-s">send alice, mac(secret_key_alice, alice)</span>
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<span class="pl-ent">bob </span><span class="pl-k">->></span> <span class="pl-ent">bob</span><span class="pl-k">:</span> <span class="pl-s">compare mac(secret_key_alice, alice) with mac(secret_key_bob, alice)</span></pre>
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</div>
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<ul>
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<li>
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Prevent forgery: without secret_key, can not generate MAC even if
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knowing <strong>a lot of</strong> alice and mac(secret_key, alice),
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</li>
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<li>Prevent collisions: keep MAC long enough (256-bit),</li>
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<li>
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Replay attacks: send transaction 2 times with perfectly MAC and u know
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why -> instead of mac(secret_key, alice), use
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<strong>counter</strong> as mac(secret_key, counter, alice).
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</li>
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<li>
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Verify must be done in <strong>constant time</strong>: if not, probably
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return error the moment the bytes differ -> attacker recreate byte by
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byte by measuring how long -> timing attacks
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</li>
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</ul>
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<p>Constant time comparison:</p>
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<div class="highlight highlight-source-go">
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<pre><span class="pl-k">for</span> <span class="pl-s1">i</span> <span class="pl-c1">:=</span> <span class="pl-c1">0</span>; <span class="pl-s1">i</span> <span class="pl-c1"><</span> <span class="pl-en">len</span>(<span class="pl-s1">x</span>); <span class="pl-s1">i</span><span class="pl-c1">++</span> {
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<span class="pl-c">// Use XOR instead of compare x[i] == y[i]</span>
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<span class="pl-c">// If x[i] == y[i] -> XOR is 1</span>
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<span class="pl-c">// Otherwise XOR is 0</span>
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<span class="pl-s1">v</span> <span class="pl-c1">|=</span> <span class="pl-s1">x</span>[<span class="pl-s1">i</span>] <span class="pl-c1">^</span> <span class="pl-s1">y</span>[<span class="pl-s1">i</span>]
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}
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<span class="pl-c">// v == 1 means all XOR is 1 means x == y</span></pre>
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</div>
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<p>Use for:</p>
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<ul>
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<li>
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Integrity: because MAC ensure no one can tamper with message without
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noticing
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</li>
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</ul>
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<div class="highlight highlight-source-mermaid">
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<pre><span class="pl-k">sequenceDiagram</span>
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<span class="pl-k">participant</span> <span class="pl-ent">alice</span>
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<span class="pl-k">participant</span> <span class="pl-ent">bob</span>
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<span class="pl-ent">alice </span><span class="pl-k">->></span> <span class="pl-ent">bob</span><span class="pl-k">:</span> <span class="pl-s">send username, password</span>
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<span class="pl-ent">bob </span><span class="pl-k">-->></span> <span class="pl-ent">alice</span><span class="pl-k">:</span> <span class="pl-s">return alice|mac(secret_key, alice)</span>
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<span class="pl-ent">alice </span><span class="pl-k">->></span> <span class="pl-ent">bob</span><span class="pl-k">:</span> <span class="pl-s">send alice|mac(secret_key, alice)</span>
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<span class="pl-ent">bob </span><span class="pl-k">-->></span> <span class="pl-ent">alice</span><span class="pl-k">:</span> <span class="pl-s">return OK</span>
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<span class="pl-ent">alice </span><span class="pl-k">->></span> <span class="pl-ent">bob</span><span class="pl-k">:</span> <span class="pl-s">send bob|mac(secret_key, alice)</span>
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<span class="pl-ent">bob </span><span class="pl-k">-->></span> <span class="pl-ent">alice</span><span class="pl-k">:</span> <span class="pl-s">return ERROR</span></pre>
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</div>
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<p><strong>HMAC</strong> is MAC using hash</p>
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<div class="markdown-heading">
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<h2 class="heading-element">AES (Advanced Encryption Standard)</h2>
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<a
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id="user-content-aes-advanced-encryption-standard"
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class="anchor"
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aria-label="Permalink: AES (Advanced Encryption Standard)"
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href="#aes-advanced-encryption-standard"
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><span aria-hidden="true" class="octicon octicon-link"></span
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></a>
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</div>
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<p>
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Currently (2023) the world using AES-128 which take a key 128 bits == 16
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bytes
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</p>
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<ul>
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<li>Take a variable-length key</li>
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<li>Take plaintext of 128 bits</li>
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<li>Give ciphertext of 128 bits</li>
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</ul>
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<p>
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AES is kind of cipher, handle fixed-size plaintext so we called
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<strong>block cipher</strong>. AES is deterministic so we can encrypt and
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decrypt.
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</p>
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<div class="markdown-heading">
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<h2 class="heading-element">AES-CBC (Cipher Block Chaining)</h2>
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<a
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id="user-content-aes-cbc-cipher-block-chaining"
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class="anchor"
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aria-label="Permalink: AES-CBC (Cipher Block Chaining)"
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href="#aes-cbc-cipher-block-chaining"
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><span aria-hidden="true" class="octicon octicon-link"></span
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></a>
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</div>
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<p>
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What if text you want to encrypt is longer than 128 bytes ? We add
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<strong>padding</strong> for text to become multi block which has 128
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bytes, then encrypt each block.
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</p>
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<p>
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Adding padding bytes is easy, remove it after decrypt is hard. How do you
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know which is padding bytes you add if you use random bytes ?
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</p>
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<p>
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Just use <strong>PKCS#7 padding</strong>. Example AES-128 use block of 16
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bytes but only have 9 bytes, should add 7 bytes padding. Just fill all
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padding bytes with padding length aka value <code>07</code>.
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</p>
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<div class="highlight highlight-text-adblock">
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<pre>XX XX XX XX XX XX XX XX XX 07 07 07 07 07 07 07</pre>
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</div>
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<p>
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So to know how much padding bytes should we remove -> read last bytes
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(<code>07</code>) to know the length to remove trailing padding bytes.
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</p>
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<p>
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The problem with naive way to split text, add padding bytes then encrypt
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each block using AES-128 is repeated text. Because it leaks information if
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text is made up from many repeated text (See
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<a href="https://words.filippo.io/the-ecb-penguin/" rel="nofollow"
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>The ECB penguin</a
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>).
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</p>
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<p>CBC = deterministic block cipher + IV (initialization vector)</p>
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<p>AES-CBC encrypt:</p>
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<ul>
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<li>IV XOR first plaintext -> AES encrypt -> first ciphertext.</li>
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<li>Use first ciphertext as IV to second ciphertext and so on.</li>
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</ul>
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<p>AES-CBC decrypt:</p>
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<ul>
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<li>AES decrypt first ciphertext -> XOR IV -> first plaintext.</li>
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<li>Use first ciphertext as IV to second block and so on.</li>
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</ul>
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<p>Because IV, same plaintext can encrypt to different ciphertext.</p>
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<p>
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<strong>WARNING</strong> If IV become predictable, AES-CBC become
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deterministic -> BEAST attack (Browser Exploit Against SSL/TLS).
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</p>
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<div class="markdown-heading">
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<h2 class="heading-element">
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AEAD (Authenticated Encryption with Associated Data)
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</h2>
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<a
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id="user-content-aead-authenticated-encryption-with-associated-data"
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class="anchor"
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aria-label="Permalink: AEAD (Authenticated Encryption with Associated Data)"
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href="#aead-authenticated-encryption-with-associated-data"
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><span aria-hidden="true" class="octicon octicon-link"></span
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></a>
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</div>
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<p>
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Because AES-CBC requires IV which shows public -> attacker can change
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IV -> lack of authenticity -> use AES-CBC-HMAC or AEAD.
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</p>
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<p>AEAD provides a way to authenticate <strong>associated data</strong>.</p>
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<div class="markdown-heading">
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<h2 class="heading-element">AES-GCM (Galois/Counter Mode)</h2>
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<a
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id="user-content-aes-gcm-galoiscounter-mode"
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class="anchor"
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aria-label="Permalink: AES-GCM (Galois/Counter Mode)"
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href="#aes-gcm-galoiscounter-mode"
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><span aria-hidden="true" class="octicon octicon-link"></span
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></a>
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</div>
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<p>... is one of AEAD implementation.</p>
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<p>AES-GCM = AES-CTR (Counter) + GMAC message authentication code</p>
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<p>AES-CTR encrypt:</p>
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<ul>
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<li>Create nonce 12 bytes (same purpose as IV).</li>
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<li>Concatenate nonce with counter 4 bytes: 1, 2, 3, ...</li>
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<li>
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Encrypt AES from concatenated none with counter to
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<strong>keystream</strong>.
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</li>
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<li>XOR keystream with plaintext -> ciphertext.</li>
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</ul>
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<p>
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Limit is counter only up to 4 bytes so only handle plaintext of 2^32 - 1
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blocks of 16 bytes aka 69 GBs.
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</p>
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<p>
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AES-CTR no need padding because if keystream is longer than plaintext, it
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is truncated to plaintext length before XOR.
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</p>
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<p>This is stream cipher, differ from block cipher</p>
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<ul>
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<li>No need padding.</li>
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<li>Ciphertext is same length as plaintext.</li>
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</ul>
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<p>GMAC is MAC with GHASH. GHASH resembles CBC mode.</p>
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<div class="markdown-heading">
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<h2 class="heading-element">ChaCha20-Poly1305</h2>
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<a
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id="user-content-chacha20-poly1305"
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class="anchor"
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aria-label="Permalink: ChaCha20-Poly1305"
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href="#chacha20-poly1305"
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><span aria-hidden="true" class="octicon octicon-link"></span
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></a>
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</div>
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<p>... is one of AEAD implementation.</p>
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<p>ChaCha20-Poly1305 = ChaCha20 stream cipher + Poly1305 MAC</p>
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<div class="markdown-heading">
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<h2 class="heading-element">Key exchange</h2>
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<a
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id="user-content-key-exchange"
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class="anchor"
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aria-label="Permalink: Key exchange"
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href="#key-exchange"
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><span aria-hidden="true" class="octicon octicon-link"></span
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></a>
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</div>
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<div class="highlight highlight-source-mermaid">
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<pre><span class="pl-k">sequenceDiagram</span>
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<span class="pl-k">participant</span> <span class="pl-ent">alice</span>
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<span class="pl-k">participant</span> <span class="pl-ent">bob</span>
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<span class="pl-ent">alice </span><span class="pl-k">->></span> <span class="pl-ent">alice</span><span class="pl-k">:</span> <span class="pl-s">generate key pair: public_key, secret_key</span>
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<span class="pl-ent">bob </span><span class="pl-k">->></span> <span class="pl-ent">bob</span><span class="pl-k">:</span> <span class="pl-s">generate key pair: public_key, secret_key</span>
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<span class="pl-ent">alice </span><span class="pl-k">->></span> <span class="pl-ent">bob</span><span class="pl-k">:</span> <span class="pl-s">send public_key</span>
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<span class="pl-ent">bob </span><span class="pl-k">->></span> <span class="pl-ent">alice</span><span class="pl-k">:</span> <span class="pl-s">send public_key</span>
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<span class="pl-ent">alice </span><span class="pl-k">->></span> <span class="pl-ent">alice</span><span class="pl-k">:</span> <span class="pl-s">generate shared_secret(secret_key, bob_public_key)</span>
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<span class="pl-ent">bob </span><span class="pl-k">->></span> <span class="pl-ent">bob</span><span class="pl-k">:</span> <span class="pl-s">generate shared_secret(secret_key, alice_public_key)</span></pre>
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</div>
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<p>
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Prevent MITM (Man In The Middle) passive attack. If attacker can intercept
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public_key then it's over.
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</p>
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<div class="markdown-heading">
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<h2 class="heading-element">Diffie-Hellman</h2>
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<a
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id="user-content-diffie-hellman"
|
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class="anchor"
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aria-label="Permalink: Diffie-Hellman"
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href="#diffie-hellman"
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><span aria-hidden="true" class="octicon octicon-link"></span
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></a>
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</div>
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<p>... is key exchange algorithm.</p>
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<ul>
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<li>
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Alice and Bob agree on prime number <code>p</code> and generator
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<code>g</code>.
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</li>
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<li>
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Alice generate secret <code>a</code> and public
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<code>A = g^a mod p</code>.
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</li>
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<li>
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Bob generate secret <code>b</code> and public
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<code>B = g^b mod p</code>.
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</li>
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<li>
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Alice and Bob exchange <code>A</code> and <code>B</code>
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<ul>
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<li>
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Same secret <code>A^b mod p == B^a mod p == g^(ab) mod p</code>
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</li>
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</ul>
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</li>
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</ul>
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<p>Diffie-Hellman is based on group theory.</p>
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<div class="markdown-heading">
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<h2 class="heading-element">Elliptic Curve Diffie-Hellman (ECDH)</h2>
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<a
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id="user-content-elliptic-curve-diffie-hellman-ecdh"
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class="anchor"
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aria-label="Permalink: Elliptic Curve Diffie-Hellman (ECDH)"
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href="#elliptic-curve-diffie-hellman-ecdh"
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><span aria-hidden="true" class="octicon octicon-link"></span
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></a>
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</div>
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<p>Instead of prime number, use elliptic curve.</p>
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<ul>
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<li>
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Alice and Bob agree on elliptic curve <code>E</code> and generator
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<code>G</code>.
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</li>
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<li>
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Alice generate secret <code>a</code> and public <code>A = [a]G</code>.
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</li>
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<li>
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Bob generate secret <code>b</code> and public <code>B = [b]G</code>.
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</li>
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<li>
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Alice and Bob exchange <code>A</code> and <code>B</code>
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<ul>
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<li>Same secret <code>[a]B == [b]A == [ab]G</code></li>
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</ul>
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</li>
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</ul>
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<div>
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Feel free to ask me via
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<a href="mailto:hauvipapro+posts@gmail.com">email</a> or
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<a rel="me" href="https://hachyderm.io/@haunguyen">Mastodon</a>.
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<br />Source code is available on
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<a href="https://github.com/haunt98/posts-go">GitHub</a>
|
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<a href="https://codeberg.org/yoshie/posts-go">Codeberg</a>
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<a href="https://git.sr.ht/~youngyoshie/posts-go">sourcehut</a>
|
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<a href="https://gitea.treehouse.systems/yoshie/posts-go">Treehouse</a>
|
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<a href="https://gitlab.com/youngyoshie/posts-go">GitLab</a>
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</div>
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</body>
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