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Vitalik Buterin, the co-founder of Ethereum, has released a new blog post discussing a new cryptographic proving system that can make zero-knowledge proofs more efficient.

The proving system, called Binius, is designed to operate directly over binary code on computers. Binary code is a language understood by computers, and it is used to store information and represents data using the symbols zero and one, otherwise known as bits.

Although there are some similarities between STARKs and Binius, Buterin explains that the mathematical tricks that enable these different proving systems are very different.

Generally speaking, STARKs is a technology that has enabled complicated statements to be easily cryptographically verified. It is designed in a way that can easily compute numbers when they are of small value, when there are large values, STARKs generate extra values, which can lead to inefficiency.

Unlike STARKs that arithmetize a statement into a polynomial equation a mathematical expression which model a relationship between variables in a block Binius treats data as a hypercube and grid, and uses multilinear polynomials to perform cryptographic proofs.

Binius converts individual values into bits and places them in a hypercube and a square. This hypercube is then converted into a grid and computations are performed in order to receive an output matrix.

A verifier will then perform its own computational calculations to ensure that the information itself matches and ensure that the compute columns returns a value claimed by the prover.

I highly encourage people to understand and explore! Lots of innovations have been happening in ZK-proving recently. And I expect lots more to come soon, Buterin wrote in an X post.

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Vitalik Buterin talks ways to make zk proofs more efficient - Blockworks