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The calculation of the Tate pairing on ordinary curves involves two major steps: the Miller Loop (ML) followed by the Final Exponentiation (FE). The first step for achieving a full pairing inversion w...
When using pairing-friendly ordinary elliptic curves to com- pute the Tate and related pairings, the computation consists of two main components, the Miller loop and the so-called final exponentiati...
Recently Tate pairing and its variations are attracted in cryptography. Their operations consist of a main iteration loop and a final exponentiation. The final exponentiation is necessary for gener...
Since the introduction of pairings over (hyper)elliptic curves in constructive cryptographic applications, an ever increasing number of protocols based on pairings have appeared in the literature....

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