Zeq Vault
An equation-based password manager. Your master equation unlocks the vault — no server ever sees your data.
How It Works
- Master Equation — You create a math equation (e.g.
x^3 + sin(y*pi) - 42.7) - Evaluation — The equation is evaluated at
x = 1.287,y = 0.777using a safe recursive descent parser - Key Derivation — The result is used as input to
PBKDF2(100,000 iterations, SHA-256) - Encryption — All vault data is encrypted with
AES-256-GCMusing the derived key - Client-Side Only — Encryption and decryption happen entirely in the browser via the Web Crypto API
The master equation is never transmitted to any server. The vault is stored as an encrypted blob in localStorage.
Encryption Details
| Parameter | Value |
|---|---|
| Algorithm | AES-256-GCM |
| Key Derivation | PBKDF2 (SHA-256, 100,000 iterations) |
| Salt | Random 16 bytes per encryption |
| IV | Random 12 bytes per encryption |
| Authentication | GCM built-in (128-bit auth tag) |
Equation Parser
The vault uses the same recursive descent parser as Equation Auth:
- 16 functions: sin, cos, tan, asin, acos, atan, sqrt, abs, log, ln, log10, exp, floor, ceil, round, sign
- 3 constants: pi, e, phi (golden ratio)
- 2 variables: x = 1.287, y = 0.777
- Operators: +, -, *, /, ^ (right-associative), unary +/-, parentheses
- No
eval()— fully safe, deterministic evaluation
Random Equation Generator
The vault includes a random equation generator with 5 complexity levels:
| Level | Example |
|---|---|
| 1 | x + 3 |
| 2 | x^2 + sin(y) |
| 3 | sqrt(x) * cos(y*pi) + 7 |
| 4 | x^3 + sin(y*pi) - floor(e * phi) |
| 5 | acos(y/x) + log(x^2 + y^2) * ceil(phi^3) - sqrt(abs(sin(x*pi))) |
Higher complexity = more entropy = stronger encryption key.
Vault Entries
Each vault entry stores:
- Service name — what the equation is for (e.g. "GitHub", "Email")
- Equation — the equation for that service
- Notes — optional text field
- Created/Modified timestamps
When you need a password for a service, enter the equation into the Zeq parser — the numeric result is your password. You can copy the result directly from the vault.
Features
Auto-Lock
The vault automatically locks after 5 minutes of inactivity. You must re-enter your master equation to unlock.
Export / Import
- Export: Downloads an encrypted backup file (
.zeqvault) - Import: Restores from a backup file — requires the correct master equation to decrypt
Strength Indicator
A visual indicator shows the strength of your equation based on:
- Number of operations
- Use of transcendental functions
- Equation length
- Diversity of operators used
Security Model
- Zero-knowledge: The server never sees your equations or vault data
- Client-side encryption: All crypto operations use the browser's Web Crypto API
- No network requests: The vault works entirely offline after initial page load
- Deterministic: Same equation always produces the same key (important for cross-device access)
- No recovery: If you forget your master equation, the vault cannot be recovered
Usage
Access the vault at /apps/zeq-vault/ or from the App Store.