import CurvePoint from "./curve-point";
import GfP12 from "./gfp12";
import TwistPoint from "./twist-point";
/**
 * miller implements the Miller loop for calculating the Optimal Ate pairing.
 * See algorithm 1 from http://cryptojedi.org/papers/dclxvi-20100714.pdf
 */
export declare function miller(q: TwistPoint, p: CurvePoint): GfP12;
/**
 * finalExponentiation computes the (p¹²-1)/Order-th power of an element of
 * GF(p¹²) to obtain an element of GT (steps 13-15 of algorithm 1 from
 * http://cryptojedi.org/papers/dclxvi-20100714.pdf)
 */
export declare function finalExponentiation(a: GfP12): GfP12;