# New Proof of Space Construction Idea

### Understanding how to use the overhead in Vector Commitments (VC)

## (1) VC PoS:

New proposition for PoS based on pairing-based VC where the replica is the precomputed proofs of openings

**Requirements:**

**space:**proofs of openings cannot be compressed - the storage required for them = storage of the full initial vector**time/cost:**proof of openings are costly to generate - a prover needs to process all vector to generate one proof

## (2) DRG PoS:

Current construction:

- first Data is sealed into Replica
- then use a VC scheme (Merkle Tree) to commit and open in the online phase

**Requirements:**

- trade-offs: we need space/time tradeoffs for the prover in the online phase
**space:**if we precompute and store proofs of openings - they should be compressible**time/cost:**if we compute proofs on the spot online: proof of openings should be efficient to generate

The two words, when based on same VC construction, are complementary: **(1) VC PoS **and **(2)** **DRG PoS **and realising one securely implies the other construction is inefficient:

**No (1)** implies **(2)**

**No (2)** implies **(1) **

- they are mutually exclusive, so if we show (1) is not possible, then this shows (2) is possible
- we need to understand in which one we are in order to use new VC for PoS
- analysing the proposition and finding ways to compress the replica or to efficiently compute the replica will lead us to an answer either showing
**(1)**is feasible or**(2)**is possible for the design we have today

### Other PoS exploration based on new VC for Replication

- Specific to PoRep optimisations and preprocessing:
- if we consider the replication protocol based on graphs as we use today, what kind of reorganisation (parents-children nodes wise) can we do to the graph
- consider pairing-based VC: how can we exploit the graph structure in order to open and check relations between nodes efficiently?