Trapdoor Pairings

Abstract

Systems and methods are described for trapdoor pairing. In one implementation, a trapdoor pairing is a cryptographic primitive generated by determining a bilinear pairing between an elliptic curve group and another group and selecting a parameter of the bilinear pairing, such as a group order or an isogeny between curves, to be a key for generating and evaluating the bilinear pairing. Trapdoor pairing allows construction of a group in which the Decisional Diffie-Hellman (DDH) problem is computationally infeasible given only the description of the group, but is easy given the secret key. Exemplary trapdoor pairing constructions have general applicability to cryptography and also lend themselves more specifically to certain special practical implementations, such as public key cryptography and certificate authority infrastructures.

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