<?xml version="1.0" encoding="utf-8" standalone="yes"?><rss version="2.0" xmlns:atom="http://www.w3.org/2005/Atom" xmlns:content="http://purl.org/rss/1.0/modules/content/"><channel><title>Passwords · XB Field Notes</title><link>https://www.xbcatm.com/tags/passwords/</link><description>Illustrated field notes on HTTP, DNS, TLS, Caddy, SSH, releases, and recovery.</description><generator>Hugo</generator><language>en-us</language><atom:link href="https://www.xbcatm.com/tags/passwords/index.xml" rel="self" type="application/rss+xml"/><item><title>Password hashes need a slow cost</title><link>https://www.xbcatm.com/posts/password-hashes-need-a-slow-cost/</link><pubDate>Thu, 10 Jun 2027 00:00:00 +0000</pubDate><guid>https://www.xbcatm.com/posts/password-hashes-need-a-slow-cost/</guid><description>快速哈希对攻击者很便利。一旦数据泄露，弱哈希方案在字库与 GPU 面前就会崩。</description><content:encoded>&lt;p&gt;You do not choose a hash for the database; you choose it for the attacker who reads the database. Dedicated password hashes trade speed for resilience so a leak does not become a password factory.&lt;/p&gt;
&lt;h2 id="fast-is-the-wrong-goal"&gt;Fast is the wrong goal&lt;/h2&gt;
&lt;p&gt;Speed is the enemy here. General-purpose hashes like SHA or MD5 run in nanoseconds and are intentionally fast, which is exactly what an offline attacker wants — they can churn through billions of guesses per second. Purpose-built password algorithms (bcrypt, scrypt, Argon2id) add a tunable cost factor plus per-user salt, so each guess costs real work (say 100ms-1s) and each account produces a different result even with a shared password. The slowness is the feature; it is what converts an instantly-downloadable hash file into a long, expensive grind. Choose an algorithm that is memory-hard where feasible, and pick a cost that stays high yet tolerable on the hardware that has to verify every login.&lt;/p&gt;
&lt;h2 id="design-for-the-day-the-copy-leaks"&gt;Design for the day the copy leaks&lt;/h2&gt;
&lt;p&gt;Design for the day the hash file leaks, because that day eventually comes. If the hashes were fast and unsalted, the attacker cracks the whole file in minutes — every weak password in the batch is gone at once. With slow, salted hashes, the same leak yields only a small fraction of the weakest passwords after real effort; the salt means identical plaintexts have different digests, so the attacker cannot amortize one guess across many accounts. Slowness plus salt and unique randomness per account is the resilience that survives the leak; there is no way back once the file is out, so the defense has to be in the stored form.&lt;/p&gt;
&lt;h2 id="agility-when-costs-change"&gt;Agility when costs change&lt;/h2&gt;
&lt;p&gt;Keep the choice in one function you can change, and plan for cost to drift upward. When you raise the work factor or move to a beefier scheme, the stored hashes carry an older cost; the pattern is to rehash on the next successful login and update the record. That keeps every account&amp;rsquo;s cost current without requiring every user to reset a password, and it means your scheme can track hardware and algorithm advances over years. The permission model of &amp;lsquo;verify with latest, refresh on login, downgrade never&amp;rsquo; should be explicit in the code, and the transition path (verified old hash -&amp;gt; new hash) must be a code path, not a manual migration.&lt;/p&gt;
&lt;h2 id="when-it-breaks"&gt;When it breaks&lt;/h2&gt;
&lt;p&gt;A single fast digest is the classic failure. SHA-256 or MD5 verifies in microseconds, so after a dump the attacker replays billions of guesses per second per GPU; weak passwords fall in hours and the whole table falls together because no per-guess cost remains. Missing salt makes it worse: identical passwords share one digest, so a single guess breaks every account that chose it, prebuilt tables transfer across breaches, and equality itself leaks who shares a password. A global salt only blocks prebuilt tables while still letting one guess test the entire file at once.&lt;/p&gt;
&lt;p&gt;A frozen cost factor is the quieter failure. Bcrypt cost 04 or PBKDF2 with a few thousand iterations may have been reasonable years ago, but hardware moved on while stored values did not. Comparison and availability break next. A plain equality check can exit on the first differing byte and expose an online timing oracle, so verification must use constant-time comparison. In the other direction, unbounded cost on the login path turns each bogus attempt into CPU you pay for; cap the maximum work, rate-limit logins, and watch for silent truncation such as the bcrypt 72-byte limit or encoding mismatches that let different inputs verify identically.&lt;/p&gt;
&lt;h2 id="check-it-quickly"&gt;Check it quickly&lt;/h2&gt;
&lt;p&gt;Save the following as &lt;code&gt;hash_cost_demo.py&lt;/code&gt; in a scratch directory and run &lt;code&gt;python3 hash_cost_demo.py&lt;/code&gt;. It uses only the standard library (&lt;code&gt;hashlib&lt;/code&gt;, &lt;code&gt;hmac&lt;/code&gt;, &lt;code&gt;os&lt;/code&gt;, &lt;code&gt;time&lt;/code&gt;), makes no network calls, and writes nothing to disk. The script contrasts fast digests against PBKDF2-HMAC-SHA256 stretching, shows two random salts give different digests for one password, and checks verification with constant-time comparison.&lt;/p&gt;
&lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-python" data-lang="python"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="s2"&gt;&amp;#34;&amp;#34;&amp;#34;Fast digest vs stretched password hash (stdlib only).&amp;#34;&amp;#34;&amp;#34;&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="nn"&gt;hashlib&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="nn"&gt;hmac&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="nn"&gt;os&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="nn"&gt;time&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;check&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ok&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;message&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="ow"&gt;not&lt;/span&gt; &lt;span class="n"&gt;ok&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;raise&lt;/span&gt; &lt;span class="ne"&gt;AssertionError&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;message&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;main&lt;/span&gt;&lt;span class="p"&gt;():&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;password&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="sa"&gt;b&lt;/span&gt;&lt;span class="s2"&gt;&amp;#34;correct-horse-123&amp;#34;&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;wrong&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="sa"&gt;b&lt;/span&gt;&lt;span class="s2"&gt;&amp;#34;correct-horse-124&amp;#34;&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;# 1. Fast hashes are cheap: time thousands of single SHA-256 digests.&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;rounds&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;5000&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;start&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;time&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;perf_counter&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;_&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nb"&gt;range&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;rounds&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;hashlib&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;sha256&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;password&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;digest&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;fast_secs&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;time&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;perf_counter&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;start&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="nb"&gt;print&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sa"&gt;f&lt;/span&gt;&lt;span class="s2"&gt;&amp;#34;fast: &lt;/span&gt;&lt;span class="si"&gt;{&lt;/span&gt;&lt;span class="n"&gt;rounds&lt;/span&gt;&lt;span class="si"&gt;}&lt;/span&gt;&lt;span class="s2"&gt;x SHA-256 in &lt;/span&gt;&lt;span class="si"&gt;{&lt;/span&gt;&lt;span class="n"&gt;fast_secs&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="mi"&gt;1000&lt;/span&gt;&lt;span class="si"&gt;:&lt;/span&gt;&lt;span class="s2"&gt;.2f&lt;/span&gt;&lt;span class="si"&gt;}&lt;/span&gt;&lt;span class="s2"&gt; ms&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;# 2. Stretching adds a tunable cost: one PBKDF2-HMAC-SHA256 derivation.&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;# Demo uses 100k iterations so it finishes instantly; production&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;# guidance asks for much more (see OWASP Password Storage).&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;salt1&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;os&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;urandom&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;16&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;salt2&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;os&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;urandom&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;16&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;check&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;salt1&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="n"&gt;salt2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="s2"&gt;&amp;#34;salts must differ&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;start&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;time&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;perf_counter&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;stored&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;hashlib&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;pbkdf2_hmac&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s2"&gt;&amp;#34;sha256&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;password&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;salt1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;100_000&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;slow_secs&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;time&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;perf_counter&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;start&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="nb"&gt;print&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sa"&gt;f&lt;/span&gt;&lt;span class="s2"&gt;&amp;#34;slow: 1x PBKDF2-HMAC-SHA256(100k) in &lt;/span&gt;&lt;span class="si"&gt;{&lt;/span&gt;&lt;span class="n"&gt;slow_secs&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="mi"&gt;1000&lt;/span&gt;&lt;span class="si"&gt;:&lt;/span&gt;&lt;span class="s2"&gt;.2f&lt;/span&gt;&lt;span class="si"&gt;}&lt;/span&gt;&lt;span class="s2"&gt; ms&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;# 3. Random per-user salt: same password, different salts, different digests.&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;other&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;hashlib&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;pbkdf2_hmac&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s2"&gt;&amp;#34;sha256&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;password&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;salt2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;100_000&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;check&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;stored&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="n"&gt;other&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="s2"&gt;&amp;#34;random salts must separate identical passwords&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="nb"&gt;print&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sa"&gt;f&lt;/span&gt;&lt;span class="s2"&gt;&amp;#34;salt separates: &lt;/span&gt;&lt;span class="si"&gt;{&lt;/span&gt;&lt;span class="n"&gt;stored&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;hex&lt;/span&gt;&lt;span class="p"&gt;()[:&lt;/span&gt;&lt;span class="mi"&gt;16&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="si"&gt;}&lt;/span&gt;&lt;span class="s2"&gt;... != &lt;/span&gt;&lt;span class="si"&gt;{&lt;/span&gt;&lt;span class="n"&gt;other&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;hex&lt;/span&gt;&lt;span class="p"&gt;()[:&lt;/span&gt;&lt;span class="mi"&gt;16&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="si"&gt;}&lt;/span&gt;&lt;span class="s2"&gt;...&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;# 4. Negative control: a global salt keeps identical passwords identical.&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;global_salt&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="sa"&gt;b&lt;/span&gt;&lt;span class="s2"&gt;&amp;#34;site-wide-salt-01!&amp;#34;&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;alice&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;hashlib&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;pbkdf2_hmac&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s2"&gt;&amp;#34;sha256&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;password&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;global_salt&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;100_000&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;bob&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;hashlib&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;pbkdf2_hmac&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s2"&gt;&amp;#34;sha256&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;password&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;global_salt&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;100_000&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;check&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;alice&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;bob&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="s2"&gt;&amp;#34;global salt must link identical passwords&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="nb"&gt;print&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s2"&gt;&amp;#34;global salt links identical passwords (do not do this)&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;# 5. Verify by re-deriving with the stored salt, using constant-time compare.&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;again&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;hashlib&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;pbkdf2_hmac&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s2"&gt;&amp;#34;sha256&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;password&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;salt1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;100_000&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;check&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;hmac&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;compare_digest&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;stored&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;again&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt; &lt;span class="s2"&gt;&amp;#34;same password+salt must verify&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;bad&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;hashlib&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;pbkdf2_hmac&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s2"&gt;&amp;#34;sha256&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;wrong&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;salt1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;100_000&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;check&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="ow"&gt;not&lt;/span&gt; &lt;span class="n"&gt;hmac&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;compare_digest&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;stored&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;bad&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt; &lt;span class="s2"&gt;&amp;#34;wrong password must not verify&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;check&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;hmac&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;compare_digest&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;stored&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;stored&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt; &lt;span class="s2"&gt;&amp;#34;compare_digest self-check&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;check&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="ow"&gt;not&lt;/span&gt; &lt;span class="n"&gt;hmac&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;compare_digest&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;stored&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;other&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt; &lt;span class="s2"&gt;&amp;#34;compare_digest mismatch-check&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="nb"&gt;print&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s2"&gt;&amp;#34;verify: correct password passes, wrong password fails&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="nb"&gt;print&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sa"&gt;f&lt;/span&gt;&lt;span class="s2"&gt;&amp;#34;ratio: one stretched hash costs ~&lt;/span&gt;&lt;span class="si"&gt;{&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;slow_secs&lt;/span&gt; &lt;span class="o"&gt;/&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;fast_secs&lt;/span&gt; &lt;span class="o"&gt;/&lt;/span&gt; &lt;span class="n"&gt;rounds&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;&lt;span class="si"&gt;:&lt;/span&gt;&lt;span class="s2"&gt;.0f&lt;/span&gt;&lt;span class="si"&gt;}&lt;/span&gt;&lt;span class="s2"&gt;x one fast digest&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="nb"&gt;print&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s2"&gt;&amp;#34;PASS: slow salted stretching beats a single fast digest&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="vm"&gt;__name__&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="s2"&gt;&amp;#34;__main__&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;main&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;p&gt;The output reports microseconds for thousands of fast hashes against milliseconds for one stretched hash, then confirms re-derivation with the same salt reproduces the stored value while a wrong password fails. The assertions passed with Python 3.12 on macOS; timings vary by machine. The demo uses reduced iterations so it finishes instantly and does not prove Argon2id tuning, GPU cost, or production rate limiting. Re-check your verifier with its documented cost parameter and a login flood budget before raising work factors.&lt;/p&gt;
&lt;h2 id="sources"&gt;Sources&lt;/h2&gt;
&lt;ul&gt;
&lt;li&gt;&lt;a href="https://cheatsheetseries.owasp.org/cheatsheets/Password_Storage_Cheat_Sheet.html"&gt;OWASP: password storage&lt;/a&gt;, slow, salted hash choices, checked 2027-06-08.&lt;/li&gt;
&lt;li&gt;&lt;a href="https://cheatsheetseries.owasp.org/cheatsheets/Cryptographic_Storage_Cheat_Sheet.html"&gt;OWASP: cryptographic storage&lt;/a&gt;, hashing vs encryption, checked 2027-06-08.&lt;/li&gt;
&lt;li&gt;&lt;a href="https://docs.openssl.org/master/man1/openssl-dgst/"&gt;OpenSSL: digest tool&lt;/a&gt;, how digests are computed, checked 2027-06-08.&lt;/li&gt;
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