Another [[ZKP/Data Marketplace/Technical Basis/Cryptographic Foundations/Mathematical Foundations|foundational element]] is the use of Quadratic Arithmetic Programs (QAPs) to encode computational logic [88]. QAPs transform a circuit's computations into a set of polynomial equations, targeting proofs of size O(log n) for circuits with n gates. This logarithmic scaling balances efficiency and security, ensuring that proof size grows minimally even as circuit complexity increases. See also: [[ZKP/Data Marketplace/Technical Basis/Cryptographic Foundations/Lifecycle of zk-SNARKs|Lifecycle of zk-SNARKs]]