Low-degree extensions refer to mathematical constructs used in polynomial arithmetic, particularly within cryptographic protocols. These extensions are essential for constructing proofs and verifying computations efficiently by operating on polynomials of limited degree. They form a basis for many advanced cryptographic schemes.
Context
In the realm of zero-knowledge proofs and verifiable computation, low-degree extensions are a critical component for optimizing proof generation and verification times. Current research focuses on developing more efficient methods for working with these extensions, especially in the context of large-scale computations. Developments to monitor include advancements in polynomial commitment schemes and their application in constructing more performant zk-SNARKs and zk-STARKs.
This research extends doubly efficient interactive proofs to arbitrary arithmetic circuits, achieving optimal linear prover time and succinct verification without requiring costly circuit layering.
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