Fable
A grain scale that only looks at total weight
Four villages wanted to train a sowing puppet together, but each village's harvest, pests, and soil quality were secrets. No one was willing to hand over the details to others. The initial approach was to send each village's ledger to the county seat to be added together. The puppet improved quickly, but the village chiefs could not sleep: the county seat had seen each family's weaknesses. Someone suggested that each village report only the puppet's improvement suggestions. But a single village's update could still reveal which field had reduced yield this year or which pest was severe. A craftsman made a new grain scale. Each village added paired masks to its own update; viewed alone they looked like random numbers, but together the masks canceled each other out.
The county only receives the sum and cannot see any village's plaintext update. Even if a few people are curious, they cannot read secrets from a single message.
The system also handles disconnections, authentication, and anomalous contributions, preventing anyone from impersonating a village or polluting the aggregate results with bad data.
The sowing puppet thus learned cross-village experience, while each village's original records and unilateral updates were not exposed to the central ledger.
On the first trial weighing, a rainstorm cut off the road to West Village and the message arrived late; another fake village sent a package of bad data under a false name. The craftsman let only villages with sufficient quantity and verified identity join this round, added the late village next round, and isolated the anomalous package first.
At the first weighing, one village arrived late, its mask could not be offset, and the total could not be computed. The craftsmen did not peek at any single village's ledger; instead they defined the rules for absence, re-reporting and verification. Only when the headcount and the masks were both complete was the county permitted to read the total weight.
At first the village chiefs still worried that the total weight might be used to infer their own situation. The craftsman had them watch the weighing process: a single message was like a stone wrapped in straw rope, and only when all the stones were put on the scale together did the straw ropes loosen each other. The county seat knew the direction, but not which household contributed which inch. Later, as more villages joined, the county seat could still only see the combined direction. The villages were willing to keep cooperating because the puppet could improve from shared experience, while a single village's soil quality and harvest were not laid out before everyone.
The village chiefs understood that collaborative training did not necessarily require handing over all their assets. The key was to let the system aggregate group signals while hiding the plaintext contributions of individual participants.