| 摘要 |
Provided are a pairing computation device, a pairing computation method, and a pairing computation program all of which enable fast pairing computation. The pairing computation device includes, where: E is an additive group of rational points on a pairable elliptic curve defined over Fpk with an embedding degree of k, and the curve equation is given by y2=x3+ax+b where a∈Fp and b∈Fp, E[r] is a set of rational points of a prime order r, &phgr;p is Frobenius endomorphism, and the order r and a trace t of the Frobenius endomorphism &phgr;p are used as functions of an integer variable χ: computation means for computing a rational function fχ,Q(S); computation means for computing a value of a rational point S(xs, ys) on a line passing through a predetermined rational point; computation means for computing a rational function f′χ,Q(S) using computation results of these computation means; and computation means for performing pairing computation by using the rational function f′χ,Q(S) as Formula (1): e(Q,S)=ƒ′χ,Q(S)(p−1)/r   (1).
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