Polylogarithmic Size

Definition ∞ In computational complexity, polylogarithmic size refers to a resource requirement, such as memory or time, that grows proportionally to a polynomial function of the logarithm of the input size. This indicates a highly efficient scaling property for algorithms or data structures, where the increase in resource usage is very slow relative to the increase in the problem’s scale. For cryptographic proofs, achieving polylogarithmic proof size or verification time is a significant objective for scalability. It is a desirable characteristic for systems processing vast amounts of data.
Context ∞ Discussions around the scalability of zero-knowledge proofs and other advanced cryptographic protocols frequently cite polylogarithmic size as a key metric for efficiency. News in theoretical computer science and blockchain research often highlights new proof systems that achieve this property, enabling the processing of larger transaction batches or more complex computations off-chain. This advancement is crucial for developing high-throughput, privacy-preserving blockchain solutions capable of supporting global-scale applications.