Ethoryx — Cryptographic Prime Generation API

Proprietary Algorithm

A multi-stage candidate-elimination procedure, formally proved. Reduces primality-test workload by 66–79% at production key sizes.

NTT & FHE Ready

Native support for NTT-compatible primes with q ≡ 1 (mod 2n). SEAL and OpenFHE compatible. 75% candidate reduction.

Security Preserved

Every prime in the target range remains reachable with uniform probability. No prime excluded, no key weakened. FIPS-relevant constant-time path.

API Endpoints

GET /v1/generate

Single prime · all sizes · drop-in

New v2.0

GET /v1/generate/rsa

RSA prime with advanced candidate optimization

New v2.0

GET /v1/generate/ntt

NTT-compatible prime · q ≡ 1 (mod 2n)

New v2.0 · Starter+

GET /v1/generate/fhe

FHE chain · SEAL / OpenFHE compatible

New v2.0 · Pro+

GET /v1/generate/rsa-pair

RSA keypair (p, q, n) · single call

New v2.0 · Starter+

GET /v1/generate/ecc

ECC prime field · NIST P-curves · params: bits (192|224|256|384|521), mod4

New v2.0 · public

GET /v1/optimize/next

Next-prime optimization · no auth required

GET /v1/verify

Primality + NTT compatibility · free

Quick Start

# NTT prime for FHE (q ≡ 1 mod 8192) curl "https://api.ethoryx.io/v1/generate/ntt?bits=256&ntt_mod=8192" -H "X-API-Key: YOUR_KEY" # Next-prime optimization (public — no auth) curl "https://api.ethoryx.io/v1/optimize/next?last_prime=1000003&last_gap=18" # FHE coefficient chain (SEAL-compatible) curl "https://api.ethoryx.io/v1/generate/fhe?n=4096&count=5" -H "X-API-Key: YOUR_STARTER_KEY"

Pricing

Free

100 calls/month
Up to 512-bit
Next-prime optimization (public)
5 calls/minute

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Starter

$29/mo

10,000 calls/month
Up to 1024-bit
FHE chains (7 primes)
NTT prime generation

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Pro ⭐

$99/mo

100,000 calls/month
Up to 2048-bit
FHE chains (20 primes)
RSA pair generation

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Enterprise

$499/mo

Unlimited calls
Up to 4096-bit
SLA guarantee
HSM integration

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