“Manuscripts don’t burn” (рукописи не горят) — made mechanical. A secret is split into n shares by a degree‑(k−1) polynomial over a small prime field; any k shares reconstruct it, burn up to n−k and the manuscript still survives. The blue team builds the threshold; the red team burns copies and lies below it.
source Mikhail Bulgakov, The Master and Margarita (written 1928–1940; first published, censored, in Moskva 1966–67) — the theme is literary (AMBER); the (k,n) threshold code is LIT. Room: THE NOVEL. Rendered as mechanism, not quoted at length.
Moscow, 1928–1940: Bulgakov writes his last novel with no hope of print. In 1930, in despair, he burned a draft himself — then began again. He dictated final edits to his wife Elena as he went blind and died in 1940.
The manuscript survived him. It reached readers in 1966–67, twenty-six years after his death, first in a censored magazine serialization, then in samizdat and abroad in full. Woland’s line to the Master — “manuscripts don’t burn” — became the book’s own history.
The novel runs on two planes at once: 1930s Moscow, where the devil Woland and his retinue expose a corrupt literary world; and ancient Yershalaim, where Pontius Pilate condemns Yeshua — a novel within the novel, the very manuscript the Master burned.
Both worlds carry the same freight: a written truth that authority wants gone, and cannot quite destroy. The engine below encodes exactly that survival as arithmetic.
Split the secret into n = 5 shares with a degree‑2 polynomial f over F257, f(0) = s. The theorem: any k = 3 shares Lagrange-interpolate back to f(0) = s — exactly. Fewer than three carry no information about s.
So the manuscript “does not burn” iff at least k of the n copies survive. Burn n−k = 2 and three remain: recovered. Burn a third and only two remain: lost. The witness (9) re-proves this on load.
Re-run the threshold live: every one of the 10 three-share subsets must recover the same secret; a two-share set must leave it undetermined (all 257 values still consistent); all modular inverses must be exact. If red accepts a below-threshold “recovery” (6), this badge turns red.
Set a secret s (the “manuscript,” a number 0–256). A fixed-seed degree‑2 polynomial f(x)=s + a₁x + a₂x² (mod 257) produces five shares (i, f(i)). Toggle each share SURVIVES / BURNED.
| share i | f(i) mod 257 | state |
|---|
With k = 3 of the 5 shares, the secret is s = Σj yj ℓj(0), the Lagrange basis evaluated at 0, all arithmetic mod 257. Below three survivors the sum is not determined by the data.
| share i | y = f(i) | ℓi(0) mod 257 | y·ℓi(0) |
|---|
Rule: recover ⇔ at least k = 3 shares survive. Any 3 give the same s; 2 give nothing.
LINEAGE. “Manuscripts don’t burn” is a claim about redundancy: truth survives if enough copies were made. That is exactly the logic of samizdat — retype it, pass it on, and no single burned copy ends it. The threshold code is the samizdat principle made exact: above k, indestructible; below it, gone.
“Manuscripts don’t burn” holds above the threshold and fails below it. Bulgakov’s own line is aspiration; the field arithmetic is where it becomes a theorem — with its exact boundary.
“Burning the only copy destroys the work.” Cut — with redundancy. If the secret was split into n=5 and k=3, burning up to two copies changes nothing; the manuscript survives. Without redundancy (one copy, k=n=1) burning it does end it — which is why Bulgakov’s 1930 fire mattered until he rewrote.
“Any surviving fragment is enough.” Cut. One or two shares recover nothing. Survival needs k, not one.
“More shares handed out ⇒ weaker secret.” Cut. Below k, extra shares still reveal nothing; the secret leaks only at the k-th.
The red move: claim a two-share recovery succeeded. Interpolate f(0) from just 2 survivors and present the number as “the manuscript.” It looks like an answer — but the witness (9) recomputes and finds the secret is underdetermined (all 257 values fit those two shares), so the claim is a fabrication and the badge turns red.
Below the threshold the “recovered” value is just the line through two arbitrary points — a different secret for every guess at the third. The attack is real, and the witness catches it.