Vitalik Buterin broke ‘Binius’ to accelerate zero knowledge proofs
Ethereum founder Vitalik Buterin discusses a new cryptographic proof system that aims to make zero-knowledge proofs more efficient.
In a blog post on April 29, Buterin described “Binius,” a highly efficient cryptographic authentication system for binary fields that aims to provide significant performance gains over traditional authentication systems such as zk-SNARKs.
Binius aims to achieve greater efficiency by performing calculations directly on individual binary bits—zeros and ones—rather than large numbers.
The inspiration behind the system stems from common cryptographic proof systems like SNARKs (Succinct Non-Interactive Argument of Knowledge) and STARKs (Scalable Clear Argument) working with large numbers such as 64-bit or 256-bit integers.
The data being processed usually consists of small values such as counters, indices and Boolean flags, but by working directly on bits, Binius can process this data efficiently, Buterin said.
According to Buterin, the new authentication system offers improvements in representing data as a multidimensional “hypercube” of bits and using binary “finite fields” to perform efficient arithmetic operations on bits and bit sequences.
It also uses a special encoding and decoding process that converts bit-level data into a form suitable for “polynomial” processing and Merkle proofs while maintaining the efficiency benefits of working in binary.
The binary system opens up significant improvements to mainstream cryptographic authentication systems, making complex cryptographic applications more efficient and scalable.
Polynomials are often used in zk-proofs to model data and calculations in a way that allows proofs to be proved without revealing the underlying data, hence the term “zero knowledge”.
Buterin demonstrates the Binius protocol with complex mathematics beyond the scope of the text, how it hides information, generates proofs, and allows verifiers to efficiently test those proofs.
Related: ZK-proofs introduce security challenges for developers
This concept was first proposed by cryptographers Benjamin E. Diamond and Jim Posen of Irreducible (formerly Ulvetana) in 1998. In a 2023 white paper entitled “Controversies surrounding the towers of binary fields.”
In general, Binius aims to deliver significant performance gains over traditional authentication systems, especially for computations involving small values and bit-level operations.
“I expect many more improvements in binary-field-based display methods in the coming months,” concluded Buterin.
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