Ever wondered how password generators create those seemingly random character strings? Let's explore the science and technology behind password generation.
The Basics of Randomness
True randomness is difficult in computers. Most password generators use 'pseudorandom number generators' (PRNG) that create sufficiently unpredictable outputs for secure passwords.
Types of Password Generators
There are three main types of password generators:
- Fully Random: Creates completely random character strings. Most secure but difficult to remember.
- Pronounceable: Generates passwords following pronunciation patterns. Easier to remember but potentially less secure.
- Passphrase: Combines random words into a memorable phrase. Good balance between security and usability.
Understanding Password Entropy
Entropy is the mathematical measure of password unpredictability. The higher the entropy, the more difficult the password is to crack. Understanding entropy helps you make informed decisions about your password security.
The Entropy Formula
Password entropy is calculated using the formula: E = L × log₂(R), where E is entropy in bits, L is password length, and R is the size of the character pool. Each additional bit of entropy doubles the number of possible combinations.
Character Pool Sizes
The character pool determines how many possible characters can appear in each position:
- Lowercase letters only (a-z): 26 characters = 4.7 bits per character
- Add uppercase letters (A-Z): 52 characters = 5.7 bits per character
- Add numbers (0-9): 62 characters = 5.95 bits per character
- Add symbols (!@#$%^&*...): 94+ characters = 6.5+ bits per character
Entropy Examples
Here's how entropy translates to real password strength:
| Password | Entropy | Time to Crack |
|---|---|---|
password |
~0 bits (dictionary word) | Instant |
abc123 |
~10 bits | < 1 second |
Tr0ub4dor |
~28 bits | ~3 hours |
X9#mK2$pQw8@ |
~78 bits | Centuries |
correct-horse-battery-staple |
~44 bits (passphrase) | ~550 years |
Recommended Entropy Levels
Security experts recommend different entropy levels based on account importance:
- Basic accounts (forums, newsletters): 40+ bits minimum
- Important accounts (social media, shopping): 60+ bits
- Critical accounts (email, banking, work): 80+ bits
- Maximum security (cryptocurrency, admin accounts): 100+ bits
Quick Entropy Calculator
To achieve 80+ bits of entropy, you need either: a 12-character password using all character types (lowercase, uppercase, numbers, symbols), or a 17-character password using only lowercase letters, or a 5-word passphrase from a 7,776-word dictionary (like Diceware).
Practical Implications
Modern password-cracking hardware can test billions of combinations per second. A password with 80 bits of entropy would take even the most powerful supercomputers longer than the age of the universe to crack through brute force. However, entropy calculations assume truly random character selection - patterns, dictionary words, and personal information drastically reduce effective entropy.
Algorithm Comparison: How Different Generators Work
Not all password generators are created equal. The algorithm used determines the security level, speed, and suitability for different applications. Here's a detailed comparison of the most common approaches.
Standard PRNG (Pseudorandom Number Generator)
Standard PRNGs like Math.random() in JavaScript create sequences that appear random but are actually deterministic. They use a mathematical formula and an initial seed value to generate numbers.
Pros:
- Very fast generation - millions of values per second
- Simple implementation, available everywhere
Cons:
- Predictable if the seed is known
- NOT suitable for security-critical applications
CSPRNG (Cryptographically Secure PRNG)
CSPRNGs like Web Crypto API (used by RndPass), /dev/urandom on Linux, or CryptGenRandom on Windows use entropy from system sources (mouse movement, keyboard timing, hardware interrupts) combined with cryptographic algorithms.
Pros:
- Cryptographically secure - unpredictable output
- Resistant to reverse engineering
- Continuously gathers entropy from system
Cons:
- Slightly slower than standard PRNG (still very fast)
Hardware Random Number Generator (HRNG)
True random number generators use physical phenomena like thermal noise, radioactive decay, or quantum effects to generate randomness. Examples include Intel RDRAND instruction and dedicated hardware devices.
Pros:
- True randomness from physical processes
- Cannot be predicted even with unlimited computing power
Cons:
- Requires specialized hardware
- Slower than software-based solutions
Diceware Method
Diceware uses physical dice rolls mapped to a wordlist of 7,776 words. Each word is selected by rolling five dice, making it completely independent of computer-generated randomness.
Pros:
- Verifiably random - anyone can audit the process
- Creates memorable passphrases
Cons:
- Manual process - slow and tedious
- Requires physical dice and wordlist
Side-by-Side Comparison
| Algorithm | Security Level | Speed | Best For |
|---|---|---|---|
| PRNG | Low (predictable) | Very fast | Games, simulations |
| CSPRNG | High (cryptographic) | Fast | Passwords, tokens, keys |
| HRNG | Highest (true random) | Moderate | Cryptographic keys, HSMs |
| Diceware | High (auditable) | Very slow | Master passwords |
Which Algorithm Should You Trust?
For everyday password generation, CSPRNG is the gold standard. It provides an excellent balance of security, speed, and availability. Hardware RNGs are overkill for most users, while standard PRNGs should never be used for passwords. Diceware is excellent for master passwords where you need maximum trust in the randomness source.
What RndPass Uses
RndPass uses the Web Crypto API, a CSPRNG implementation built into modern browsers. This API is standardized, audited by browser vendors, and meets the security requirements for generating passwords, encryption keys, and other cryptographic material. Your passwords are generated with the same level of randomness used by banks and government agencies.
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How Our Generator Works
RndPass uses a cryptographically secure random number generator in your browser. Here's the process:
- You specify your requirements (length, character types)
- The generator creates a set of allowed characters based on your selection
- A secure random function selects characters from this set
- The process repeats until the desired length is reached
Security Considerations
Not all password generators are created equal. Here's what to look for:
- Client-side generation - passwords should not be sent to a server
- Cryptographically secure randomness - not just Math.random()
- Open source - the community can audit the security code
Best Practices
For maximum security, use passwords with at least 16 characters including all character types. Store generated passwords in a password manager and never share them insecurely.