Plasma Cash with Sparse Merkle Trees, Bloom filters, and Probabilistic Transfers

The power of Bloom filters is that they can compress a large amount of hashes with no false negatives but some expected probability of false positives along the way depending on the filter size. So you should consider the case of a miner “maliciously” publishing the hash in the Bloom filter but not the SMT root as a false positive, as if the transaction is never published.

Big picture, however, I believe consensus will emerge that all previous conceptual use of Bloom filters in Plasma Cash will be replaced with RSA Accumulator non-membership proofs in Plasma Prime (but the SMT key-value data structure remains) – see RSA Accumulators for Plasma Cash history reduction and Plasma Implementers Call #17 - (R)eally (S)uper (A)wesome Episode. Actual Plasma implementers have several subproblems eg in mapping/hashing integer Coin IDs to primes to work out to make this ideas real, but we’ll have concrete implementations soon.