Our Tool: Cryptographic Accumulator

A public state cryptographic accumulator is a cryptographic data structure that allows for the compact and efficient representation of a dynamic set of values, such that anyone can verify whether a particular value is a member of the set without having to reveal the entire set.

To verify a compute node exists in our set we deploy our accumulator as a wasm-based smart contract. It keeps a constant-size for the identities(hash of the identity key) independent the size of the group, and then we use membership proofs to verify them in constant time when fetching our contract from state. Consensus validators will be allowed to produce a proof of correct execution over the results of the computation if the compute node proves its identity exists within the accumulator.

Note that the hash of the group public keys are published in the accumulator but this can be made confidential. A group signature over the identity keys is used in constructing a block: these are ring-signatures built over the HyperSDK to ensure this is privacy preserved.