Understanding Password Cryptography

Modern password security relies on mathematical principles derived from information theory and cryptographic analysis. Password strength is quantified through entropy calculations, measured in bits, where each additional bit doubles the computational complexity required for brute-force attacks. This generator uses the Web Cryptography API's getRandomValues() method, a cryptographically secure pseudorandom number generator (CSPRNG) that sources entropy from hardware random number generators when available, meeting NIST SP 800-90A standards for deterministic random bit generation.

Unlike simpler generators that rely on Math.random(), our implementation produces output that is computationally indistinguishable from true random sequences, ensuring that generated passwords exhibit no predictable patterns exploitable through cryptanalytic attacks. The entire process runs client-side in your browser -- no passwords are ever transmitted, stored, or logged on any server.

How Password Entropy Works

Password entropy is calculated using the formula H = log2(N^L), where N is the character set size and L is the password length. Character set selection directly influences entropy through base-N logarithmic scaling, with each expansion increasing the search space exponentially:

• Lowercase only (26 chars) - 4.7 bits of entropy per character
• Mixed case (52 chars) - 5.7 bits per character
• Alphanumeric (62 chars) - 5.95 bits per character
• Full printable ASCII (94 chars) - 6.55 bits per character, the maximum this generator offers

Passwords below 40 bits of entropy are vulnerable to distributed computing attacks within hours. Moderate entropy (40-59 bits) resists individual attackers but remains vulnerable to coordinated efforts. Strong passwords (60-79 bits) are computationally infeasible for most threat actors, while very strong passwords (80+ bits) withstand even state-level computational resources for decades.

Defending Against Modern Attack Vectors

Cryptographically generated passwords eliminate vulnerabilities exploited by dictionary-based attacks through uniform distribution across the entire character space. Modern authentication systems implement hash functions with computational delay mechanisms such as PBKDF2, bcrypt, scrypt, and Argon2 to mitigate offline brute-force attacks. Current OWASP recommendations specify minimum 600,000 iterations for PBKDF2-SHA256, requiring proportionally higher entropy for equivalent security margins.

Password security also degrades over time due to advancing computational capabilities. A password with 60 bits of entropy that is secure against current hardware becomes vulnerable to technology a decade from now. Security practitioners recommend generating passwords with entropy 50-100% above current requirements to account for these advances and potential quantum computing threats, where Grover's algorithm effectively halves password entropy.

Best Practices for Password Management

Generating a strong password is only the first step. Proper storage and management are equally critical to maintaining security:

• Use a password manager - Encrypted databases with master key derivation functions provide the most secure storage for generated passwords
• Never reuse passwords - Each account should have a unique, independently generated password to prevent credential stuffing attacks
• Enable multi-factor authentication - Even cryptographically strong passwords become vulnerable to phishing and social engineering; supplement with FIDO2/WebAuthn, TOTP authenticators, or hardware security keys
• Consider the similar-character trade-off - Excluding visually similar characters (0/O, 1/l/I) reduces entropy by approximately 8-12% but significantly improves usability for passwords that must be typed from visual reference
• Aim for 16+ characters - For general applications, 16-20 characters using mixed character sets provide 95-130 bits of entropy, sufficient against projected computational advances for 20-30 years