A low-depth polynomial refers to a polynomial function that can be computed using a small number of arithmetic operations or a circuit with a limited number of layers. This characteristic is significant in computational complexity theory and cryptographic constructions. It implies efficiency in computation. This property enhances performance.
Context
In zero-knowledge proofs and other advanced cryptographic protocols used in blockchain scaling solutions, low-depth polynomials are highly desirable for optimizing proof generation and verification times. Efficient polynomial representation directly impacts the feasibility and cost-effectiveness of privacy-preserving transactions. Research efforts aim to design cryptographic primitives that leverage such computationally light structures.
A new general-purpose Zero-Knowledge Streaming Interactive Proof (zkSIP) achieves negligible error, enabling robust, stateless verification over massive data streams.
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