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Atrum is a parimutuel pool, not an order book. That is not a preference or a simplification — it is the only mechanism that works under the constraint.

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The constraint

Atrum uses additively-homomorphic encryption. Given two ciphertexts the contract can compute the encryption of their sum, without ever learning either value. That is what lets a pool total exist while individual stakes stay hidden. What it cannot do is compare. There is no operation that takes two ciphertexts and tells you which is larger.

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Why that rules out an order book

Order matching is comparison. Is this bid at least the ask? Every matching engine ever written is built on that question. A contract that can add but not compare cannot match orders. So:
  • No order book. Matching is comparison.
  • No AMM. Pricing curves need to compare a trade against reserves.
  • Parimutuel. Everyone stakes into a pool, and winners split it pro rata. Payouts need only addition and one division at settlement — no comparison at any point.
This is why nobody has retrofitted privacy onto an existing prediction market. It is not that it would be difficult; the market design itself has to change.

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Everyone hits this wall

Look at what private trading systems actually do:
  • Penumbra batches trades into sealed auctions.
  • Renegade matches inside multi-party computation.
  • Atrum pools.
Nobody runs a private continuous order book in production, because continuous matching leaks by construction whatever cryptography is underneath.

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What parimutuel costs you

Being honest about the trade:
  • No live price to trade against. You stake; you do not take a quote.
  • No partial fills or limit orders. You are in the pool or you are not.
  • Odds move after you commit. Later money changes your payout, and you cannot react.
That last one is real and it is not fixed by better cryptography — it is a property of the mechanism. A bettor who is right early is diluted by money that arrives later.

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Would FHE change this?

In principle yes. Fully homomorphic encryption permits arbitrary computation on ciphertexts, including comparison, so an encrypted order book becomes expressible. Expressible is not practical. Comparison is the expensive FHE operation, and matching one order against a resting book needs many of them. The realistic first version is a periodic batch auction, not continuous matching — which is, again, a form of batching. FHE also does not remove the need for a decryption committee. It relocates the trust; it does not delete it.