Why Polynomial Commitments Might Be a ‘Breakthrough’ for Ethereum 2.0

The Ethereum community now has a roadmap, albeit a confusing one.

Dropped Wednesday, Ethereum co-founder Vitalik Buterin’s state of the network map helps contextualize the next five to ten years for a global community of 20,000 developers while highlighting a key issue for the blockchain’s next version: scalability.

The Eth 2.0 research team is now leaning into a new concept called “polynomial commitments” to reduce the data used per computation on the network, according to a March 17 blog post by researcher Danny Ryan.

Dubbed “magic math” by Buterin, polynomial commitments are being eyed as a way to verify the state of the network at low computational cost, a key goal of the future network.

Still, Buterin’s map tags his magic math for network integration not until at least the third phase in the multi-year push to Eth 2.0.

“Polynomial commitments could be the major breakthrough we’ve been looking for,” Ryan said, specifically regarding the storage of account data in the next version of Ethereum.

The Ethereum Foundation did not respond to a request for comment by press time.

Magic math

Polynomial commitments are similar to the polynomials we all came to learn and love in elementary school: a math expression with both variables and coefficients (i.e., Y=2X).

But, again, this is magic math so it’s not quite so simple.

Buterin describes polynomial commitments as “a sort of ‘hash’ of some polynomial P(x) with the property that you can perform arithmetic checks on hashes.” The original paper on polynomial commitments, meanwhile, synthesizes the math scheme as “six algorithms” that show proof of an event occurring with as little computing data as possible.

“We suggest replacing Merkle trees by magic math called “polynomial commitments” to accumulate blockchain state,” Buterin said in the Ethereum Foundation blog post. “Benefits include reducing the size of stateless client witnesses (excluding contract code and state data) to near…

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