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Vitalik Buterin via the Vitalik Buterin Blog This is a mirror of the post at https://medium.com/@VitalikButerin/exploring-elliptic-curve-pairings-c73c1864e627 Trigger warning: math. One of the key cryptographic primitives behind various constructions, including deterministic threshold signatures, zk-SNARKs and other simpler forms of zero-knowledge proofs is the elliptic curve pairing. Elliptic curve pairings (or "bilinear maps") are a recent addition to a 30-year-long history of using elliptic curves for cryptographic applications including encryption and digital signatures; pairings introduce a form of "encrypted multiplication", greatly expanding what elliptic curve-based protocols can do. The purpose of this