The messenger that doesn’t just lock your conversations — it proves the lock still works. Live entropy verification, post-quantum encryption, VoiceGuard voice indicators, and Guardian protection — on your device.
Every encryption key starts with random numbers. If those numbers aren't truly random, your encryption is silently compromised.
Two years. Millions of servers. Only 32,768 possible keys.
Nobody noticed.Hundreds of millions of Android phones. Hardware RNG degraded silently.
Nobody noticed.NSA backdoor in network equipment. Generator looked perfectly random.
Nobody noticed.Shannon entropy — the industry standard — reports 7.999 out of 8.000 for all of them.
Perfect score. Catastrophic security.
Every byte of randomness passes through four independent quality tests — continuously, in real time, on your device. If anything degrades, you know immediately. Not in two years. Now.
No other messaging app does this.
| Generator | Shannon | Verdict | PL (engine) | Verdict |
|---|---|---|---|---|
| OS /dev/urandom | 7.999 | ✓ Pass | z = +0.3 | ✓ Healthy |
| IBM RANDU (1969) | 7.999 | ✓ Pass | z = −301 | ⚠ Critical |
| 16-bit LFSR | 8.000 | ✓ Pass | z = −328 | ⚠ Critical |
| glibc rand() | 7.999 | ✓ Pass | z = +4.6 | ⚠ Critical |
Most apps show a lock icon. APPEIRON shows the actual health of your encryption engine — because a lock means nothing if the key was generated from weak randomness.
From a trusted circle of two to an entire organization — APPEIRON scales privacy without selling your data.
Create your organization in-app, generate APEIRO-ORG codes, and onboard members in seat packs. One code activates Team for the whole group.
Point every team member at the same relay URL automatically. Lock it so nobody drifts to an unknown server — your infrastructure, your rules.
Invite someone you trust to be your Guardian. Silent alarm, encrypted location on demand, and automatic alerts when a call shows sustained stress or voice mismatch.
Server stores only ciphertext. Shamir shards split the vault key across contacts you choose. Lose a phone — recover with shards, not with us reading your data.
APPEIRON is a privacy messenger for individuals and organizations. Subscriptions unlock features — they are not separate apps. Team is an organizational layer on top of Pro+; Groups are how people chat together.
Follow the path that matches what you need. One app — five levels.
Team and Guardian both build on Pro+ — they are parallel branches, not “one includes the other”.
| Feature | Group (chat) | Team (organization) |
|---|---|---|
| Purpose | Encrypted conversation & group calls | Company membership, licenses, relay policy |
| Who creates it | Any user with contacts | Org admin (Team tier) |
| Add members | Invite contacts / share invite link | Share APEIRO-ORG code → redeem in app |
| Contacts required first? | Usually yes (or invite link) | No — directory sync adds org members automatically |
| Admin powers | Group admin: roster, invites | Org admin: seats, relay preset, remove member |
| Group video call | Yes — group audio/video conference (3+, Pro+; any member can start) | Via Groups (Team supplies people, not the call UI) |
| Relay control | Each user's relay | Optional org-wide preset & lock |
Individuals, families, anyone starting out
E2E chat (PQ hybrid), 1:1 calls, groups, disappearing messages, Proof-of-Read (Seal), Entropy Health Monitor, Quantum Burn, 13 languages, anonymous ID, media editor
One-time $3.99. Full encryption. No ads. No data selling.
Quantum Vault and Mesh require Pro.
Power users who need secure storage and offline mesh
Everything in Base + Quantum Vault, Mesh/Nearby, DMS basics
Encrypted document vault and peer radar when infrastructure fails.
Journalists, executives, high-risk personal use
Everything in Pro + duress PIN & decoy vault, advanced DMS / backup options, Tor path & Direct link, group conference (3+; any member can start), chat polls
Maximum personal protection and encrypted recovery without trusting us with plaintext.
Companies, teams, NGOs — 5 to hundreds of seats
Everything in Pro+ + org admin, APEIRO-ORG codes, directory sync, relay preset & lock; screen share & polls
Onboard staff without QR scanning; optional managed relay or your own server (BYO).
Default: APPEIRON managed relay. Opt-out: admin sets your wss:// URL.
Families / partners needing mutual protection
Everything in Pro+ + Guardian (silent alarm, consent location, VoiceGuard, optional stress auto-alarm) — no Team org admin; screen share in calls
Family protection without surveillance. VoiceGuard in calls. No company admin panel.
Base is a one-time purchase ($3.99) via the App Store (iOS). Pro, Pro+, Team, and Guardian are auto-renewable App Store subscriptions. Cancel anytime in your Apple ID settings; the tier reverts when the subscription ends. Android billing will follow the Google Play release.
Subscriptions include a 7-day free trial. Base is a one-time purchase ($3.99).
USD prices. Annual plans save ~2 months.
L0: OS Entropy — Hardware RNG via operating system. Where every other app stops, we continue.
L1: Arithmetic Lattice — 64 primes form a 2D quasicrystal. Baker's theorem (1966) guarantees it never repeats. Shor's algorithm requires periodicity — no period, no attack.
L2: HKDF-SHA3-256 — Cryptographic extraction using SHA-3, not SHA-2. Different math foundation. Block size: 136 bytes.
L3: Hedging — Output = AR XOR HKDF. Either source strong = output strong. Both must fail simultaneously.
L4: Pool Feedback — HMAC-SHA3 ensures forward secrecy. Past outputs cannot be reconstructed.
Phase Locking (4 scales) — 8, 16, 24, 32-bit residue coverage. RANDU: z = −301. Shannon: 7.999. Memory: 32 KB.
Gap Spectrum — Temporal byte recurrence distribution. Catches what PL might miss.
Adaptive Threshold — Self-learning per-device baseline. Anti-poisoning. RAW_SAFE floor.
PQ Validator — Bias + correlation + block uniformity for ML-KEM, ML-DSA, SLH-DSA.
Symmetric: ChaCha20-Poly1305 • KDF: HKDF-SHA3-256 • Key exchange: X25519
Wire: 12B nonce || ciphertext || 16B tag • Pool: HMAC-SHA3-256 • Zeroize on Drop
Engine: Rust. Memory-safe. No garbage collector. 39 tests, 0 failures.
Entropy validated for all NIST PQ standards: ML-KEM-768, ML-DSA-65, SLH-DSA-128s.
Hybrid ML-KEM-768 + X25519 key exchange is live in every chat today. An attacker must break both layers.
The AR lattice is Shor-resistant by construction. Baker's theorem proves it has no period.
WebRTC + TURN: Encrypted calls use peer-to-peer WebRTC with our own TURN server. Default mode routes media through TURN so both IP addresses stay hidden.
VoIP Push: Incoming calls wake the app even when it is asleep — PushKit on iOS, encrypted signaling on the relay.
Encrypted Backup API: Relay stores ciphertext blobs only (POST /backup). Server never sees vault plaintext.
Team Relay Control: Admins can preset and lock the relay URL for all organization members.
| Signal | Telegram | Threema | APPEIRON | ||
|---|---|---|---|---|---|
| E2E Encryption | ✓ | ✓ | Partial | ✓ | ✓ |
| No Ads | ✓ | — | — | ✓ | ✓ |
| Entropy Monitoring | — | — | — | — | ✓ |
| PQ Readiness | — | — | — | — | ✓ |
| Encrypted Vault | — | — | — | — | ✓ |
| Mesh / P2P | — | — | — | — | ✓ |
| Proof-of-Read Certificates | — | — | — | — | ✓ |
| Caller Voice Verification | — | — | — | — | ✓ |
| Dead Man's Switch | — | — | — | — | ✓ |
| PQ Hybrid Key Exchange (live) | Partial | — | — | — | ✓ |
| Guardian / Silent Alarm | — | — | — | — | ✓ |
| Team Org & Relay Control | — | — | — | — | ✓ |
| Shamir Vault Recovery | — | — | — | — | ✓ |
| SHA-3 | — | — | — | — | ✓ |
Signal set the bar for private messaging. APPEIRON raises it — with entropy you can see, voice you can verify, and protection you can extend to the people who matter most.
Changed byte in ciphertext → decryption fails. Wrong key → error, not random data. Wire: 12B nonce || ciphertext || 16B Poly1305 tag.
RANDU: z = −301. LFSR: z = −328. glibc: z = +4.6. Shannon reports 7.999 for all — blind. OS urandom: correctly healthy, zero false alarms.
0 false alarms in 250 windows. CSPRNG → RANDU transition: detected in first 8 KB. Anti-poisoning baseline drift: 0.0000 after 20 attack windows.
Encrypted vault backups are ciphertext-only on the relay. Shamir shard restore never exposes the vault key to the server. Wrong shard combination fails — no silent corruption.
We cannot prevent the recipient from capturing their screen. Disappearing messages are best-effort.
If your phone is rooted or has system-level malware, no app can protect you.
If a nation-state has physical access to your device, we cannot guarantee security.
PL detects strong algebraic structure. It does not detect gradual mixing of good and bad RNG below 100% substitution.
Every product that claims to be “unbreakable” is lying. Security is a spectrum, not a switch. We tell you exactly where our defenses are strong and where they end — because informed users make better decisions than users who believe in magic.
APPEIRON's cryptography engine rests on original research in number theory, quantum chaos, and applied security — published in 2025 and engineered into production code.
The founding paper. Connects Baker's theorem to five domains of information science. 6 theorems, 23 references, 1121 lines.
Published 2025Stadium billiard experiments: prime potentials protect time-reversal symmetry (GOE statistics) under perturbations.
Published 2025The bridge paper: transfers PL test from quantum physics to cryptographic engineering. Theorem + proof + validation.
Published 2025Spectral perturbation analysis. Super-Poisson variance 1.48 at 13.9σ significance.
Published 2025PL test applied to IBM Quantum 127-qubit hardware. Detects per-qubit bias invisible to Shannon entropy.
Published 2025APPEIRON was born from a simple observation: every encrypted messaging app in the world trusts its random number generator blindly. If that generator fails — hardware degradation, supply chain compromise, deliberate backdoor — the encryption is silently compromised. Nobody knows. Sometimes for years.
We decided to build a messenger that doesn't just encrypt messages, but continuously verifies that the encryption is actually working — at the mathematical level, in real time, on your device.
The core technology is based on the Arithmetic Rigidity framework — connecting prime number theory, quasicrystal mathematics, and quantum chaos to practical information security. The Phase Locking test originated in quantum physics and was transferred to cryptographic engineering. Validated on IBM Quantum hardware and verified with 39 automated tests.
APPEIRON is developed by Cascade Investment LLC — building privacy technology that earns trust through mathematics, not marketing promises.
Contact:
Download on the App Store for iPhone and iPad. Choose Base ($3.99 one-time) or a subscription with a 7-day free trial inside the app. Android is not on Google Play yet — request the beta via Contact.
Need help with Team seats, Guardian setup, or gift codes?