The Role of Polynomial Obligations in the Development of Ethereum 2.0

Vitalik Buterin proposed creating a new roadmap for Ethereum 2.0., which in his opinion should be a huge push forward in creating a new version of network.

Why should this be a breakthrough? According to experts, polynomial obligations can reduce the amount of data used for calculations in the network, which is an important advantage.

The main goal that developers want to achieve in the next version of the blockchain is to consider polynomial commitments as a way to check the network status as low computational costs.

## Magic Math

Magic mathematics is polynomial commitments, which are similar to polynomials from mathematics variables with a certain coefficient. Specifically these calculations will help to get everything you need about the state of blockchain, and it will not increase the size of the client’s witnesses that don’t fix the state but reduce it to almost zero.

## The State of Blockchain

Introduction of ETH 2.0., as Danny Ryan said, is great, but a promising idea because a completely new field is being touched upon, which requires a tremendous amount of time to devote complex tasks, to study new technologies.

Blockchains record both inputs and outputs. Those main 2 outputs are:

- The account-based model (Ethereum uses it; each block of ETH contains evidence —the Merkle tree).
- The unspent output model (uses Bitcoin).

The concept of introducing polynomial obligations is just one of many. Moreover, it is still at the research stage, so that we will hope that all ideas will be realized in reality!