Ethoryx Cipher generates deterministic key bits from the interference pattern between adjacent Riemann zeta zeros. Each bit is computed from the spectral power ratio of two zeros at a specific grid width. The sequence is reproducible by anyone with the Tesfa Grid engine — but unpredictable without it.
A new cryptographic primitive discovered in the Tesfa-Zeta Conjecture research.
Adjacent Riemann zeta zeros (e.g., γ₄ = 30.42 and γ₅ = 32.94) produce spectral peaks that oscillate in dominance as the Tesfa Grid width C changes. At some C values γ₄ dominates (R > 1); at others γ₅ dominates (R < 1). This oscillation is deterministic.
For each C value, the spectral power ratio R is computed. R > 1 produces bit 1. R < 1 produces bit 0. Stepping through C values produces a binary key sequence. The key is deterministic — anyone with the same grid parameters gets the same bits.
Predicting the key without computing the Tesfa Grid requires either brute-forcing all possible beat pair × C-range × step-size combinations, or independently discovering the spectral structure of primes. The security assumption is fundamentally different from RSA or Diffie-Hellman.
# Generate a 7-bit key from γ₄/γ₅ beat pair
curl -X POST "https://api.ethoryx.io/v1/cipher/key" \
-H "Content-Type: application/json" \
-d '{"pair":"g4_g5","c_start":10000,"c_step":50000,"n_bits":7}'
# Response
{
"key_binary": "1111001",
"key_hex": "f2",
"R_values": [
{"C": 10000, "R": 1.257, "bit": 1},
{"C": 60000, "R": 3.064, "bit": 1},
{"C": 110000, "R": 5.260, "bit": 1},
{"C": 160000, "R": 3.640, "bit": 1},
{"C": 210000, "R": 0.608, "bit": 0},
{"C": 260000, "R": 0.463, "bit": 0},
{"C": 310000, "R": 1.358, "bit": 1}
],
"generation_time_ms": 842.3,
"engine": "Ethoryx Spectral Engine"
}Instead of time-based key rotation, advance the C parameter by a shared step size. Each step produces a new key bit. The key schedule is driven by the structure of primes, not by a clock. Both parties compute independently and arrive at the same key.
Four beat pairs produce four independent key streams. Use γ₄/γ₅ for the data channel, γ₁/γ₂ for the control channel, γ₃₄/γ₃₅ for authentication, γ₄₅/γ₄₆ for integrity. Each pair has different oscillation characteristics.
The security of beat-cipher keys does not depend on the hardness of factoring or discrete logarithms. It depends on the computational cost of the Tesfa Grid spectral engine. This makes it a candidate for post-quantum key agreement — subject to formal cryptanalysis.
The beat frequency phenomenon is documented in Volume II of the Tesfa Grid research programme. Academic researchers can reproduce all results with the open-source V6 engine. The API provides convenient access without local computation.
Starter plan ($29/mo) includes 7-bit keys. Pro plan ($99/mo) includes 32-bit keys with full spectral access.
Every call produces a cryptographically unique key. The server generates a session nonce, derives a unique set of computation parameters, and runs the full mathematical engine. No two calls return the same key. Share the nonce with your peer to reproduce the same key on their side.