I want a cryptographic accumulator[^accumulator] that has the following properties:
- It can be build incrementally using a small amount of persistent memory
- Witness proofs are reasonably small.
- Witness proofs are computationally easy to verify.
- Must have at least 100-bit security.
The idea is to minimize on-chain storage; the accumulator will live on-chain, maintained by a smart contract. Transactions submitted to the smart contract can add to the accumulator. And then later transactions can be created that include proofs that a value is part of the accumulator.