The messenger that doesn’t just lock your conversations — it proves the lock still works. Live entropy verification, post-quantum encryption, voice fraud detection, and Guardian protection — all on your device, all the time.
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 |
Double Ratchet with post-quantum hybrid key exchange (ML-KEM-768 + X25519). ChaCha20-Poly1305, SHA-3, Sealed Sender. Not even we can read your messages.
Encrypted calls with P2P WebRTC where possible, TURN fallback where not. VoIP push wakes the app even when it's asleep.
On-device voiceprint verification of the person you're talking to, plus a live stress index. Detect voice fraud — nothing leaves your phone.
Cryptographically signed read receipts (Ed25519). Tap the seal to see a verifiable certificate of exactly when your message was read.
Real-time verification of your device's random number generator. See your security score. Know it's real.
Encrypted storage for documents, photos, audio, video, passwords and cards. Duress PIN, decoy vault. Physical Burn overwrites with entropy, not just deletes.
Hybrid ML-KEM-768 + X25519 key exchange is live in every chat — not a roadmap item. Entropy validated for ML-KEM, ML-DSA, SLH-DSA.
If you don't check in, APPEIRON acts: burn the vault, notify contacts, or send an encrypted backup. Duress PIN and Shamir options included.
Peer-to-peer when the internet is down. Relay, Nearby, or Offline. Radar shows peers around you.
30 seconds to 30 days. Physical Burn overwrites with cryptographic entropy — forensic recovery impossible.
Trim video, crop and annotate photos before sending — native AVFoundation pipeline, no third-party upload.
Anonymous identity — no phone number or email required. Fully localized in 13 languages.
Mutual consent protection for someone you care about. Silent alarm, one-time encrypted location, in-call voiceprint match and stress alerts — without surveillance.
Create an organization, issue seat-pack codes, set a shared relay URL, and optionally lock it so every member stays on your infrastructure.
Pro+ can store ciphertext-only vault backups on your relay. Shamir secret sharing splits the vault key across trusted contacts — recoverable without trusting the server.
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.
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: info@cascadeinvestment.llc
APPEIRON is in private beta. Public App Store and Google Play links will appear here after release. Until then, request early access by email.