Definition ∞ Linear functions are mathematical relationships where the output is directly proportional to the input, represented graphically as a straight line. In cryptography and blockchain, they are used in various algorithms, including hash functions, error-correcting codes, and linear algebraic operations within zero-knowledge proofs. Their predictability and simplicity are leveraged in specific cryptographic constructions. These functions are foundational in constructing verifiable computations.
Context ∞ Linear functions are integral to the underlying mathematical operations within many cryptographic schemes that secure digital assets and transactions. Their role in constructing efficient and verifiable proofs, such as those used in SNARKs and STARKs, is a subject of ongoing research and optimization. Understanding their application helps clarify the computational aspects of advanced blockchain technologies.
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