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Explain the TOTP algorithm
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Quantum
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index.html
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index.html
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<link rel="icon" type="image/svg+xml" href="/totp.svg"/>
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<link rel="shortcut icon" href="/favicon.ico"/>
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<link rel="apple-touch-icon" sizes="180x180" href="/apple-touch-icon.png"/>
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<meta name="apple-mobile-web-app-title" content="TOTP.lol"/>
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<meta name="apple-mobile-web-app-title" content="TOTP.fyi"/>
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<link rel="manifest" href="/site.webmanifest"/>
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<meta name="viewport" content="width=device-width, initial-scale=1.0"/>
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<title>TOTP.lol — A TOTP Code Generator for Developers</title>
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<title>TOTP.fyi — A TOTP Code Generator for Developers</title>
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</head>
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<body>
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<nav class="navbar navbar-expand-lg">
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<div class="container">
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<a class="navbar-brand" href="#">TOTP.lol</a>
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<a class="navbar-brand" href="#">TOTP.fyi</a>
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<button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbarSupportedContent"
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aria-controls="navbarSupportedContent" aria-expanded="false" aria-label="Toggle navigation">
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<span class="navbar-toggler-icon"></span>
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<li class="nav-item">
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<a class="nav-link" href="#how-to-use">How to use?</a>
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</li>
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<li class="nav-item">
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<a class="nav-link" href="#how-does-it-work">How does it work?</a>
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</li>
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<li class="nav-item">
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<a class="nav-link" href="#support-me">Support me</a>
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</li>
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directly to a certain configuration.</p>
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</div>
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</div>
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<div class="card">
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<div class="card-body">
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<h3 class="card-title" id="how-does-it-work">How does TOTP work?</h3>
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<p class="card-text">Time-based one-time password (TOTP), defined in <a
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href="https://datatracker.ietf.org/doc/html/rfc6238">RFC 6238</a>, is based on the HMAC-based one-time password
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(HOTP) algorithm, which uses the common HMAC construction based on the current time. TOTP requires the following
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inputs:
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</p>
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<ul class="card-text">
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<li>The cryptographic hash function <var>H</var>, which defaults to SHA-1. This is configurable in the advanced
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settings;
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</li>
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<li>The secret key <var>K</var>, which is commonly encoded as Base32. This value, encoded in Base32, is what you
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enter into the <strong>secret key</strong> field;
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</li>
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<li>The time window <var>X</var>, which is how long each code is valid for;</li>
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<li>The epoch <var>T<sub>0</sub></var>, which is the Unix epoch (0 in Unix time) in every known implementation,
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but could be changed; and
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</li>
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<li>The number of digits <var>d</var>, which is the length of the final output code in decimal digits.</li>
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</ul>
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<p class="card-text">The algorithm is as follows:</p>
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<ol class="card-text">
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<li>Take the current unix time <var>U</var>;</li>
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<li>Compute the time step count
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<img class="math" src="math/t.svg" alt="T=\left\lfloor\frac{U - T_0}{X}\right\rfloor" height="40">;
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</li>
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<li>Compute the HMAC <img class="math" src="math/h.svg" alt="h = \text{HMAC}_H(K, T)" height="18">;</li>
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<li>Extract the 4 lowest order bits, i.e. the 4 least significant bits from the last byte of <var>h</var>, to
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create the integer <var>i</var>;
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</li>
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<li>Take four bytes from <var>h</var> starting at <var>i</var>, i.e. bytes [<var>i</var>, <var>i</var>+4), mask
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off the most significant bit (to support signed arithmetic), and use it to create the integer <var>y</var>;
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and finally
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</li>
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<li>Compute the code as <img class="math" src="math/mod.svg" alt="y \bmod{10^d}" height="18"
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style="vertical-align: -3px">.
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</li>
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</ol>
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<p class="card-text">To avoid clock synchronization issues, most implementations will accept TOTP codes from the
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window before and after the one based on the current time. This tool lets you see the previous and next codes to
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help you debug.</p>
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</div>
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</div>
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<div class="card">
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<div class="card-body">
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<h3 class="card-title" id="support-me">I like this website. How can I support you?</h3>
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{
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"name": "TOTP.lol",
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"name": "TOTP.fyi",
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"short_name": "TOTP",
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"icons": [
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{
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