NEW IACR ePrint paper published → arXiv: tesfadereth

RSA primes,
66–79% faster.
Formally proved.

TesfahSec uses a proprietary mathematical approach — formally proved and independently verified — to generate cryptographic primes with far fewer primality tests. As key sizes grow, the savings compound.

Get started free → Read the paper GitHub ↗

install

pip install tesfagrid

79%

Fewer primality tests

at 1024-bit RSA · measured

66%

Fewer primality tests

at 2048-bit RSA · measured

348K

verified gaps · 0 violations

3×

independent run verification

How it works

Smarter candidate selection.
Same security. Less work.

Standard prime generation searches blindly. TesfahSec uses a formally proved approach to generate only valid candidates — before any expensive test runs.

01 / 04

◈

Proprietary pre-filter

A formally proved mathematical constraint eliminates numbers that cannot be prime before any computation begins. No guessing. No wasted iterations. Derived from the Tesfa Grid geometric framework.

Formally proved · Tesfa Grid

02 / 04

⊛

Multi-layer elimination

Additional screening layers further reduce the candidate pool before any primality test is called. Each layer is mathematically justified — not heuristic. The result: 66–79% fewer primality tests.

66–79% test reduction · measured

03 / 04

⊕

Deterministic primality test

Only validated candidates reach the final primality test. We use the industry-standard witness set — deterministically correct for all practical RSA key sizes. Same certainty. Reached faster.

Deterministic · no false positives

04 / 04

🔐

Full unpredictability preserved

Every prime is selected from a cryptographically random start. The pre-filtering only removes impossible candidates — every valid prime remains reachable with equal probability. Security is unchanged.

CSPRNG random · uniform distribution

Side by side

Standard vs TesfahSec

The same prime. A fundamentally different path to find it.

STANDARD Blind random search

Pick a completely random number

No mathematical knowledge applied. Any integer in the bit range is a candidate, including the vast majority that cannot be prime.

Basic filtering — skip even numbers

The only mathematical knowledge applied: even numbers are not prime. Eliminates 50% of candidates. Still leaves most composites untouched.

Run expensive primality test

Miller-Rabin primality test runs on the candidate. At 2048-bit, this is called approximately 836 times before a prime is found. Most calls return composite.

~836 Miller-Rabin tests at 2048-bit
Most work is wasted on impossible candidates

TESHFAHSEC Proof-guided generation

Apply proprietary pre-filter

A formally proved constraint — derived from the Tesfa Grid — instantly eliminates numbers that cannot be prime. No computation required. No valid prime is missed.

Additional screening layers

Further mathematically justified filters reduce the candidate pool. Combined, the multi-layer approach eliminates up to 79% of integers before any primality test runs.

Run the same primality test

Identical Miller-Rabin test — but called only on candidates that have already passed all pre-filters. At 2048-bit, called approximately 282 times. Same prime found.

~282 Miller-Rabin tests at 2048-bit
−66% work. Same prime. Same security.

Benchmark

Three machines. One result.

Miller-Rabin test count is machine-independent — it measures algorithmic work. Verified independently on two machines with 150 total trials.

512-BIT

512-bit

Standard184 tests

TesfahSec41 tests

−78%

1024-BIT · MAX REDUCTION

1024-bit

Standard511 tests

TesfahSec108 tests

−79%

2048-BIT · NIST STANDARD

2048-bit

Standard836 tests

TesfahSec282 tests

−66%

NIST recommended

Method	Run 1	Run 2	Run 3 · independent	Avg	vs Standard
Standard baseline	213	194	194	200	—
Standard+ (basic opt.)	245	112	112	156	−22%
TesfahSecour method	84	61	61	69	−66%

512-bit primes · 150 total trials · theorem compliance 100% on all generated primes

↗

DigiCert and Microsoft are transitioning to 3072-bit and 4096-bit RSA. Miller-Rabin cost scales as O(bits³) — each test becomes exponentially more expensive at larger key sizes. TesfahSec savings compound as the industry moves to larger keys. At 4096-bit, each primality test is 512× more expensive than at 512-bit. Our 66%+ reduction is worth more with every bit added.

Who benefits

Built for production security

Any system generating RSA or ECC keys benefits. The larger the key, the greater the savings.

🏛

Certificate Authorities

Millions of TLS certificates issued, each requiring RSA prime generation. At 2048-bit: 554 fewer primality tests per certificate. At scale across millions of certificates, compute savings are measurable.

−66% compute per certificate at 2048-bit

⚙

HSM Manufacturers

Hardware security modules generate RSA keys continuously. TesfahSec reduces computation per key and eliminates timing variability in candidate generation — a property valued in FIPS-compliant implementations.

Constant-time generation · FIPS-relevant

🏦

Financial Technology

Every secure API call, digital signature, and encrypted transaction uses RSA or ECC. Companies upgrading to 3072-bit for NIST compliance need efficient, formally proved prime generation at scale.

REST API · drop-in · no code change

⌨

Developers and Researchers

Any application generating RSA keys benefits. Open-source Python library for integration. REST API with a free tier for testing and small projects. Academic paper for those who need the formal proof.

pip install tesfagrid · 100 free calls/month

API Reference

One header. One endpoint.
A prime in milliseconds.

REST API, zero dependencies, any language.

GET

/v1/generate

Generate a prime · 256 to 4096-bit

GET

/v1/generate/rsa-pair

Full RSA keypair (p, q, n) · Pro+

GET

/v1/verify

Verify primality · all tiers · free

GET

/v1/status

Health check · no auth required

Or use the library

from tesfagrid import prime_generator
p, tests = prime_generator.generate(bits=2048)
# tests = 282 vs ~836 standard

GET /v1/generate

# Request
curl "https://tesfagrid.io/v1/generate?bits=2048" \
  -H "X-API-Key: tg_pro_your_key"

# Response
{
  "prime": "9821374956...",
  "bits": 2048,
  "miller_rabin_tests": 282,
  "generation_ms": 142.3,
  "calls_remaining": 99718
}
      

Pricing

Start free. Scale as you grow.

Same quality at every tier. Cancel any time.

Free

100 calls / month

Up to 512-bit primes
5 calls / minute
/v1/verify included
Email support

Get free key →

Starter

$29_/mo

10,000 calls / month

Up to 1024-bit primes
30 calls / minute
Usage dashboard
Email support

Start →

Formally proved security

Security proof published on IACR ePrint and arXiv. Every generated prime is drawn from the full distribution with equal probability. No prime excluded.

⏱

No timing side-channel

Constant-time candidate generation — no variable rejection loop. Critical for hardware security modules and FIPS compliance environments.

↗

Open source foundation

Core algorithm MIT-licensed on GitHub. Full source available. The API adds infrastructure — not secrecy. Inspect everything.

Research

The mathematics is published

IACR ePrint and arXiv. Complete security proof. All benchmark data. Seven sections.

Tesfa Grid Sieve: Theorem-Guided Prime Generation — Tesfaye Dereje, JFS, 2026

IACR ePrint → Research hub → GitHub →

RSA primes, 66–79% faster. Formally proved.

Smarter candidate selection.Same security. Less work.