Logarchéon · MSIA Encryption

MSIA Encryption Tool

Set your key, type a message, and press Encrypt. The scrambled code can only be read by someone with the same key and settings. Everything runs on your device — nothing leaves your browser.
New here? Start with the tutorial ← · U.S. Patent Pending 64/067,703 · Source

Set the key — same for sender and reader. Tap Load demo key or type your own numbers.
Encrypt — blue box: type message → Encrypt → Copy the code.
Decrypt — gold box: same key + settings → paste code → Decrypt.

Initializing…

Strength (generators)

Mode (precision)

Hide method (extra lock)

How hard is it to crack? (changes with your settings)

Number of possible keys

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Time to crack — normal computer

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fastest computers today

Time to crack — future quantum computer

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① Send a secret message

Put in your key, type your message, and press Encrypt. You'll get scrambled code to copy and send.

Step 1 · Your secret key — the numbers

These boxes are your key. Tap Load demo key for a ready-made one, or type your own numbers (decimals and negatives are fine). The page shows a green check when the numbers work. (Advanced: each box-set is a 2×2 generator matrix; each must be hyperbolic — its two corner-to-corner numbers add to more than 2, or less than −2.)

Fill the boxes, or tap Load demo key.

Step 2 · Your message

Type anything — any language, emoji, or symbols.

message size: 0 / 64

Step 3 · Scramble it

Scrambled code — copy this and send it

Your scrambled code will appear here. Send it to your friend along with the key and settings.

② Read a secret message

Use the same key and settings the sender used, paste their scrambled code, and press Decrypt.

Step 1 · The same secret key

Enter the exact same numbers the sender used. If even one is different, it won't open. (And set the same Strength and Mode at the top.)

Enter the same numbers the sender gave you.

Step 2 · The scrambled code

Paste the code your friend sent, or open their saved file.

Open a saved file

Step 3 · Open it

The message

The secret message will appear here.

Notes

Pure algebraic (Sparse)

not secure as-is

Decryption by Vandermonde inversion of power-sum traces — no hash. Mathematically closest to the bare construction; not cryptographically secure on its own and carries no authentication.

Hashed FO-KEM (this demo)

authenticated

Lengths → SHA-512 → 256-bit key, XOR keystream, HMAC-SHA-512 tag. Gives authentication (CCA2-style). Security rests on SHA-512; the geometric hardness (Option B) is the open research direction.

Brute-force & quantum resistance

Each generator adds four real key parameters (~97 bits at High precision). At High + g≥3 the geodesic keyspace exceeds the 256-bit derived key, so SHA-512's Grover floor of 2¹²⁸ dominates — the NIST quantum-safe bar.

config	key space	classical	quantum (Grover)	quantum-safe?
Standard g=2	2⁶¹	~21 min (nation-state)	instant	no
High g=2	2¹⁹⁴	> age of universe	~10⁶ yr	no (2⁹⁷)
High g=3	2²⁵⁶ (SHA-capped)	> age of universe	> age of universe	yes (2¹²⁸)
High g≥4	2²⁵⁶ (SHA-capped)	> age of universe	> age of universe	yes (margin)

Offline & air-gapped use

All computation runs locally in your browser. Once loaded, no network is needed — disconnect Wi-Fi and encrypt/decrypt still work.

Choosing the key

Each number may be positive or negative and need not be a whole number. Each generator must be hyperbolic: its two diagonal numbers add to more than 2 or less than −2, checked live.

Algebraic constructions — companion matrices & trace recovery

The tool above uses the hashed FO-KEM path. The constructions here demonstrate the algebraic core of MSIA directly: each character’s count becomes a companion block of x^ℓ−·1; the blocks are assembled by block-diagonal concatenation and disguised by a random diagonal similarity D^−¹1AD; and for the pure-algebraic variant, decryption recovers the message by solving the Vandermonde system from the power-trace vector T — no hash involved.

Construction

Generators

Encryption key — generator matrices

The key is a set of 2×2 generators. Each must be hyperbolic: |trace| > 2. Lengths ℓ are derived from these, exactly like the tutorial. Three generators deepen the key space — a ciphertext made with 3 must be decrypted with 3.

G1 (T₁)

G2 (T₂)

Message0 / 128 bytes

Ciphertext object (JSON)

Companion structure (chunk 1)

Decrypt console — paste or upload a ciphertext

A clean station for the receiving side. Paste a JSON ciphertext (or upload the saved file) and decrypt it on its own — the variant and generator count are read from the object, and the companion structure is shown as it recovers the message.

Ciphertext object (JSON)

Recovered message

Companion structure (chunk 1)

Research proof-of-concept. MSIA is not an accredited or independently audited cipher. Security numbers measure SHA-512 and Grover resistance (Option A). For any sensitive use, operate only within procedures accredited by your own organization.