The mathematical basis of [[ZKP/Data Marketplace/Technical Basis/Cryptographic Foundations/Lifecycle of zk-SNARKs|zk-SNARKs]] includes elliptic curves, specifically BLS12-381 curves, which facilitate pairing operations (e.g., e(G_1, G_2)) [88]. These pairings enable the construction of succinct proofs, a critical feature for verification efficiency. [[ZKP/Data Marketplace/Intro|The Data Marketplace]] utilizes the BLS12-381 curve due to its security characteristics and implementation efficiency within the cryptographic infrastructure. This curve provides approximately 128-bit security against discrete logarithm attacks while enabling efficient pairing computations required for [[ZKP/Data Marketplace/Technical Basis/Cryptographic Foundations/zk-SNARKs and Privacy Framework|zk-SNARK verification.]] See also: [[ZKP/Data Marketplace/Technical Basis/Cryptographic Foundations/Polynomial Commitments via QAPs|Polynomial Commitments via QAPs]]