FibroHash presents a cryptographically secure password generation framework implementing industry-standard PBKDF2-HMAC-SHA256 key derivation combined with Python's cryptographically secure random number generator (CSPRNG). This research contribution addresses password security in system administration environments through comprehensive entropy analysis and security validation methodologies. The framework demonstrates secure password generation using established cryptographic primitives with proper salt handling and quality assessment protocols. The implementation operates entirely offline using Python's standard library, eliminating external dependencies and potential network-based security vulnerabilities. Research contributions include:• Implementation of configurable PBKDF2-HMAC-SHA256 iterations (1,000-10,000 rounds)• Multi-round HMAC-based entropy generation methodology• Comprehensive entropy analysis tools with Shannon entropy calculations• Password quality validation framework with security scoring algorithms• Reproducible testing suite for cryptographic validation• Programmatic interfaces for integration into security research workflows Empirical analysis demonstrates measured entropy levels from 78 bits (20-character passwords) to 361 bits (64-character passwords), with standard 32-character passwords achieving 155 bits of entropy. All entropy measurements derive from actual character distribution analysis rather than theoretical maximums, providing accurate security assessments for research applications. Technical architecture encompasses:• PBKDF2-HMAC-SHA256 key derivation with configurable iteration parameters• Multi-round HMAC sequence generation for enhanced cryptographic strength• Extended 90+ character charset for maximum per-character entropy• Integrated security analysis including pattern detection and entropy measurement• Self-contained implementation requiring no external dependencies Research applications include system administration password security, cryptographic entropy analysis, educational cryptography instruction, and integration into larger security research frameworks. This work provides empirically validated entropy measurements based on actual password generation and character distribution analysis, contributing to accurate security assessment methodologies in password generation research.