Qatsi: Stateless Secret Generation via Hierarchical Memory-Hard Key Derivation

We present Qatsi, a hierarchical key derivation scheme using Argon2id that generates reproducible cryptographic secrets without persistent storage. The system eliminates vault-based attack surfaces by deriving all secrets deterministically from a single high-entropy master secret and contextual layers. Outputs achieve 103-312 bits of entropy through memory-hard derivation (64-128 MiB, 16-32 iterations) and provably uniform rejection sampling over 7776-word mnemonics or 90-character passwords. We formalize the hierarchical construction, prove output uniformity, and quantify GPU attack costs: $2.4 \times 10^{16}$ years for 80-bit master secrets on single-GPU adversaries under Paranoid parameters (128 MiB memory). The implementation in Rust provides automatic memory zeroization, compile-time wordlist integrity verification, and comprehensive test coverage. Reference benchmarks on Apple M1 Pro (2021) demonstrate practical usability with 544 ms Standard mode and 2273 ms Paranoid mode single-layer derivations. Qatsi targets air-gapped systems and master credential generation where stateless reproducibility outweighs rotation flexibility.