Entropy and attack speed analysis

How Strong Is Your PDF Password? Entropy, Attack Speeds, and Safe Patterns

Password strength is not a feeling. It is a measurable quantity with a direct dollar cost to attackers. This guide shows how entropy is calculated, how fast modern GPUs grind each PDF encryption version, which memorable patterns are truly strong versus fake-strong, and what the recovery implications look like if you forget. The goal is to give you enough numeric intuition to pick a password you will keep using for years.

Bottom line if you just want the answer

Generate a 14-character random password from a password manager, using lowercase, uppercase, digits, and symbols. Apply it with AES-256 encryption. That combination produces about 92 bits of entropy and sits comfortably beyond current and foreseeable attack capacity. Store the password in the manager, not in your head.

Entropy: the only strength metric that matters

Password strength is measured in bits of entropy. Entropy captures the attacker's uncertainty about the password. A password with 40 bits of entropy can be found, in the worst case, by trying 2^40 candidates, which is about one trillion. A password with 60 bits of entropy requires 2^60 attempts, about one quintillion. Every additional bit doubles the difficulty.

For a random password drawn uniformly from an alphabet of size N, the entropy per character is log2(N). Lowercase English gives 4.7 bits per character, mixed case gives 5.7, adding digits gives 5.95, and including common symbols gives about 6.6 bits per character. Multiplying by the length gives total entropy. A 10-character password from the full 72-character alphabet has 10 times 6.17, or about 62 bits of entropy.

The catch is that this formula only applies when the password is actually random. A password you invent with your brain is not random, because your brain prefers certain patterns, and attackers know those patterns. We will return to this below.

Entropy per length chart

LengthLowercase only (26)Mixed case (52)+ digits (62)+ symbols (72)
6 chars28.2 bits34.2 bits35.7 bits37.0 bits
8 chars37.6 bits45.6 bits47.6 bits49.4 bits
10 chars47.0 bits57.0 bits59.5 bits61.7 bits
12 chars56.4 bits68.4 bits71.4 bits74.0 bits
14 chars65.8 bits79.8 bits83.3 bits86.3 bits
16 chars75.2 bits91.2 bits95.2 bits98.7 bits

Read this chart as a planning tool. If you need 60 bits of entropy, 10 mixed-case-plus-digits characters is enough. If you want 80, go to 14 characters with any alphabet. If you want truly comfortable margin, 16 characters with symbols is far beyond anything attackers can currently grind through.

GPU attack speeds per PDF encryption version

The entropy number only matters when compared against real-world attack speed. Different PDF encryption versions slow down attackers by different amounts. A modern eight-GPU rig loaded with NVIDIA RTX 4090 or equivalent cards achieves approximate speeds as follows. Speeds are rounded and for orientation only:

EncryptionHashcat modeSpeed (8-GPU rig)60-bit password time
PDF 1.1-1.3 (40-bit RC4)1040010+ GH/sN/A: keyspace is tiny
PDF 1.4-1.6 (128-bit RC4)10500~5 GH/sDecades if truly random
PDF 1.7 AES-12810700~2 GH/sCenturies if random
PDF 1.7 Ext. 3 AES-25610500/10700 variants~1 GH/sMillennia if random
PDF 2.0 AES-25610700~500 MH/sMillennia if random

The last column assumes truly random passwords. With dictionary words, common patterns, or short inputs, attackers reach the target in minutes or hours regardless of the encryption. The encryption version only buys you time proportional to the entropy of the password you chose. Our success rates article has empirical numbers on how often weak passwords are cracked in practice.

Fake-strong patterns that attackers target first

The gap between theoretical and practical strength is where most real-world PDFs get broken. Attackers do not try random strings in lexicographic order. They try the patterns that humans actually use, in the order of their frequency. A password that looks complex to you may be in the top 0.001% of a dictionary that attackers grind through in the first hour. The list below shows common fake-strong patterns and why they fail:

Capitalized word plus digits plus punctuation

Password123! looks like 11 characters with four character classes. In reality it is a word from a small dictionary with an obvious suffix. This pattern is the first thing every attacker tries. Effective entropy is closer to 14 bits than to 60.

Name plus birth year

John1985 or Smith2001 combines public information attackers can collect with a trivial variation. For targeted attacks, this pattern is checked in the first thousand candidates. It provides almost no security.

Leet-speak substitutions

P@ssw0rd is a dictionary word with predictable letter swaps. Attack rules in hashcat apply leet substitutions automatically, so these do not expand the attacker's work at all.

Keyboard walks

Qwerty123 or 1qaz2wsx are patterns on the keyboard. Specialized walk generators produce every variation in a few megabytes, and every password cracker ships with them built in.

Personal phrase with spaces

My dog Max was born 2015 looks like 25 characters of prose. A phrase of common English words has very low per-word entropy, and a four- or five-word phrase drawn from natural English is often under 30 bits. Random words from a large list are fine; remembered phrases are not.

Patterns that are actually strong

Randomly generated strings

The gold standard. 14 random characters from a 72-character alphabet gives 86 bits. A password manager generates these for free. You do not need to memorize them.

Diceware-style passphrases

Six or seven random words from the EFF long list. Each word adds about 12.9 bits. A six-word passphrase has about 77 bits of entropy. The words are easy to type and moderately easy to memorize. The key requirement is that you pick the words with a real random source, not by thinking up words.

Letter-from-phrase construction

Take the first letter of each word in a personally meaningful sentence and include case and punctuation. TwiDotCiw@14tWbA for The whale in the Dot Com is with a Whale by Any name works as a memorable password, though the entropy depends on the quality and uniqueness of your sentence. Less reliable than diceware but better than a single word.

Recovery implications: the decision tree

If you choose a truly strong password, you are committing to remembering it or trusting the password manager that stores it. AES-256 PDFs with 80-plus bits of entropy cannot be brute-forced, not by you and not by anyone offering to recover the file. The cryptography is doing its job. The flip side is that losing the password means losing access to the document forever.

A useful mental model:

Low stakes: convenience protection only

Use a password you will not forget, even if it is not theoretically strong. The file is only protecting against casual inspection, not a determined attacker. Recovery is trivial if you forget it, and the file does not contain secrets worth stealing anyway.

Medium stakes: real content to protect

Use a random 10-to-12-character password generated and stored by a password manager. Entropy around 60-70 bits keeps the file safe from opportunistic attackers. Recovery is very unlikely if you lose the manager, which is why backing up the manager properly matters more than the password itself.

High stakes: protection against serious attackers

14-plus random characters, AES-256, stored in a password manager with a recovery kit printed and kept in a safe. The password is unrecoverable if you lose the manager and the printed backup. The file is as secure as PDF technology permits.

Our forgot PDF password page walks through the realistic recovery paths for each encryption version and password strength level.

Practical recommendations by use case

Use caseEncryptionPasswordWhere to store
Bank statement to family memberAES-128Shared phraseAgreed in advance
Medical record personal archiveAES-25614 char randomPassword manager
Corporate contractAES-256 (PDF 2.0)16 char randomEnterprise vault
Legal filingsAES-256 + signingDiceware 7-wordManager + paper backup
Casual document sharingAES-128Anything not trivialRemember directly

Common myths debunked

Myth: Long passwords always beat short ones. Length matters, but only when the characters are independently random. A 20-character English phrase you invented yourself has less entropy than a 10-character random string.

Myth: Changing passwords frequently helps. Forcing users to change passwords often leads to weaker passwords, because people adapt by picking simpler ones that are easier to rotate. A single strong password is more protective than a rotating series of mediocre ones.

Myth: Numbers and symbols always improve a password. Only if they add actual randomness. Password2024! is not stronger than Password because the 2024! suffix is in every attacker's dictionary.

Myth: AES-256 alone is enough. Strong encryption with a weak password is broken in minutes. The encryption algorithm is only as strong as the weakest part of the system, which is almost always the password.

Myth: Two passwords on one PDF doubles security. User and owner passwords protect different things. Adding an owner password does not make the user password harder to break. If an attacker recovers the user password, the content is exposed regardless of whether an owner password is set.

The most common real-world failure

Users pick a strong-looking password, never write it down, and forget it within a year. They then cannot access their own files. A strong password must be paired with a reliable storage mechanism, otherwise it becomes a denial-of-service attack on yourself. Use a password manager.

Final recommendation

Use AES-256, use a 14-character random password from a password manager, and back up the password manager. That single combination covers 99% of realistic threats while keeping recovery possible when you, not an attacker, need access.

Read next

For the engineering detail on how PDF passwords are actually used, see how PDF encryption works. For a breakdown of encryption versions, see PDF encryption types. For empirical recovery success rates by password quality, read success rates.