Keys from the
prime number spectrum
Every key is unique, 256-bit strong, and derived from a published mathematical proof — the Tesfa Grid spectral atlas, proven across 11 data points from C = 10,000 to C = 10,000,000.
10K → 10M grid width
p < 10⁻¹⁵
HKDF-SHA256 · RFC 5869
C = 10K · 50K … 10M
How spectral key derivation works
Three layers combine. Each contributes independently. No single layer alone is sufficient.
Your account's secret C
A secret spectral seed is derived for your account at registration. The server maps it to a unique C value in the Tesfa atlas range — never revealed, always re-derived.
C = HMAC(MASTER_SECRET, seed)
30-dimensional spectral fingerprint
The server looks up your secret C in the spectral atlas — 30 alignment errors between Tesfa prime residual peaks and exact Riemann zeta zero frequencies. Proven to ±0.005 precision.
δ[30] · 240 bytes · z = +7.953
Unique key every request
A 256-bit random salt is generated per request. Your delta vector is mixed with the salt and request context through HKDF-SHA256 producing a fresh key every time.
key = HKDF(δ_bytes, random_salt, ctx)
Try it right now
Paste your API key and generate a real spectral key. Run it twice — the keys will be different every time.
Generate spectral key
Authorization: Bearer <key>
Content-Type: application/json
// Click "Generate key" to call the live API
// Your key is derived from the Tesfa Grid
// prime spectral atlas · z_analytic = +7.953
What provides the security
Each layer contributes independently. The combination is what makes Spectral KDF unique.
Secret C — per-account entropy
Your C is derived from HMAC(MASTER_SECRET, spectral_seed) and never stored or returned. Without MASTER_SECRET an attacker cannot enumerate your C. 9.9M possible values.
Random salt — per-request uniqueness
A fresh 256-bit salt is generated for every key request via os.urandom(32). No two requests ever produce the same key, even same account same purpose.
Delta vector — mathematical structure
240 bytes of spectral data at your secret C. Proven: z_analytic = +7.953 invariant, 30/30 significance at all 11 C values. Published in Tesfa-Zeta Volume IV (2026).
Where to use Spectral KDF
Any context needing unique session keys, auditable key derivation, or mathematically structured entropy.
Session key generation
Replace static shared secrets with a fresh 256-bit spectral key per session. Each key is unique and tied to your account's spectral identity.
Regulated industry audit trails
Banking, government, compliance — key provenance required. Every Spectral KDF key can be re-derived server-side with full mathematical documentation.
Encryption key bootstrapping
Use Spectral KDF output as seed for AES-256 or ChaCha20 encryption. Mathematically provable structure above standard random key generation.
API-to-API authentication
Derive short-lived access tokens between services using a shared spectral address. Both sides derive the same key from a shared nonce — no secret transmission.
Start deriving spectral keys
Free tier includes 100 spectral key requests per month. Enterprise plans include dedicated spectral seeds and audit log access.