High degree custom gates refer to specialized logical operations within a cryptographic circuit that involve polynomials of higher mathematical degrees. These gates are designed for specific computational tasks in zero-knowledge proof systems, extending beyond simple binary operations. They allow for more complex calculations to be expressed efficiently within the arithmetization process, which converts a computation into a polynomial form. The high degree aspect indicates that the polynomials representing these gates have exponents greater than one, offering greater expressive power.
Context
The implementation of high degree custom gates is a critical area of research and development in optimizing the performance of advanced zero-knowledge proof protocols. Their efficient design can significantly reduce the computational resources required for proving and verifying complex statements on blockchain networks. Current efforts focus on creating new custom gates that can speed up common operations in decentralized applications, thereby enhancing scalability and reducing transaction costs.
HyperPlonk eliminates the FFT bottleneck in Plonk by using multilinear polynomials over the boolean hypercube, enabling linear-time ZK-proof generation for massive circuits.
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