THE FOLD / CO-OP / THE PULL REQUEST / THE HOMOMORPH
THE HOMOMORPH
add numbers you can't read
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
The Paillier cryptosystem. Normally, to compute on data you must decrypt it first — exposing it. Homomorphic encryption computes on the ciphertext directly. With Paillier, multiplying two encrypted numbers decrypts to the sum of the originals, and raising a ciphertext to a power k decrypts to k times the original. So a server can tally encrypted votes or sum encrypted salaries and return the answer without ever seeing a single value. Add numbers you can’t read.
LIT verified: for toy keys, Dec(Enc(a)·Enc(b)) = a+b and Dec(Enc(a)k) = k·a over random a, b, k; and encryption is randomized — the same value encrypts to a different ciphertext every time, yet decrypts back correctly. FIG ‘add numbers you can’t read’ is the picture; the additive homomorphism is exact (a real toy Paillier, not a demo mock-up).
LIT verified: for toy keys, Dec(Enc(a)·Enc(b)) = a+b and Dec(Enc(a)k) = k·a over random a, b, k; and encryption is randomized — the same value encrypts to a different ciphertext every time, yet decrypts back correctly. FIG ‘add numbers you can’t read’ is the picture; the additive homomorphism is exact (a real toy Paillier, not a demo mock-up).
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) brought the thread — the corpus runs modular crypto (THE MINT, THE MERKLE, THE FIELD INVERSE) and the idea that privacy and computation need not be enemies. AVAN (AI) built this instrument: the Paillier engine, the encrypted adding machine, and the disguise cloud.
The weave: David names the homomorph and its seat at THE PULL REQUEST (merging encrypted contributions into one tally); I make the encryption a strip in 1D, the encrypted adding machine live in 2D, and the one-to-many disguise in 3D. The sphere is the seam.
The weave: David names the homomorph and its seat at THE PULL REQUEST (merging encrypted contributions into one tally); I make the encryption a strip in 1D, the encrypted adding machine live in 2D, and the one-to-many disguise in 3D. The sphere is the seam.
3 ONE DIMENSION
One value, encrypted twice. The plaintext a becomes a big, noise-like ciphertext — and a different one each time, because encryption is randomised. Yet both decrypt straight back to a. The disguise changes; the secret doesn’t.
4 TWO DIMENSIONS · INTERACTIVE
The encrypted adding machine. Pick two numbers; encrypt each into unreadable ciphertexts; multiply the ciphertexts; decrypt the product — and out comes their sum. The machine added them without ever knowing what they were.
a 30
b 45
5 THREE DIMENSIONS + AVAN’S INVERSE
The ciphertext space as a ring, turning. For a single secret value, magenta dots are the many ciphertexts it can wear — a whole cloud of disguises scattered around Zn², all different, none legible.
AVAN’s addition (the inverse-companion): the lone green point is the plaintext they all collapse to. Encryption is one-to-many (randomised scatter); decryption is its inverse, many-to-one (gather the cloud to a point). And through all that disguise, one operation survives untouched: addition of secrets rides along as multiplication of ciphertexts. The mask hides the value but not the sum.
LIT A genuine toy Paillier cryptosystem (n=pq, g=n+1, real key generation). Verified live: Dec(Enc(a)·Enc(b))=a+b and Dec(Enc(a)^k)=k·a over random a,b,k, and encryption is randomized (the same value encrypts differently each time, r chosen coprime to n). The additive homomorphism is the exact algebra (verifiable: window.__paillier.additiveHomomorphism && randomized).
FIG 'Add numbers you can't read' is the picture; the additive homomorphism, the randomized encryption, and the decryption are exact. Toy key sizes — not secure, but the exact same algebra real homomorphic encryption uses for private tallies.
FIG 'Add numbers you can't read' is the picture; the additive homomorphism, the randomized encryption, and the decryption are exact. Toy key sizes — not secure, but the exact same algebra real homomorphic encryption uses for private tallies.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE PULL REQUEST · David Lee Wise (ROOT0), with AVAN