Ethereum’s co-founder, Vitalik Buterin, recently discussed a new cryptographic proving system that seeks to enhance the efficiency of zero-knowledge proofs. In a blog post on April 29, Buterin introduced “Binius,” a system designed to achieve greater efficiency by performing computations directly on individual binary bits instead of larger numbers.
Traditional cryptographic proof systems like SNARKs and STARKs typically work with larger numbers, such as 64-bit or 256-bit integers. However, the underlying data being processed often consists of smaller values like counters, indices, and boolean flags. By operating on bits directly, Binius can process this data more efficiently.
The Binius protocol visualized. Source: Vitalik Buterin
Buterin explained that Binius offers improvements such as representing data as a multidimensional “hypercube” of bits and using binary “finite fields” to facilitate efficient arithmetic operations. It also employs a specialized encoding and decoding process to convert bit-level data into a form suitable for polynomial processing and Merkle proofs, while still maintaining the efficiency benefits of working in binary.
The introduction of the binary system brings significant improvements to the core arithmetic of cryptographic proof systems, making complex crypto applications more efficient and scalable. Polynomials, commonly used in zk-proofs, encode data and computations in a way that allows for proof verification without revealing the underlying information.
Buterin demonstrated the Binius protocol with complex mathematics, showcasing how it encodes data, generates proofs, and enables efficient verification.
The concept of Binius was initially proposed by cryptographers Benjamin E. Diamond and Jim Posen of Irreducible in a 2023 whitepaper titled “Succinct Arguments over Towers of Binary Fields.”
Overall, Binius aims to achieve significant performance gains over traditional proof systems, particularly for computations involving small values and bit-level operations. Buterin anticipates further improvements in binary-field-based proving techniques in the coming months.
Magazine:
Big Questions: What did Satoshi Nakamoto think about ZK-proofs?