Importance

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Abstract

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 aεFp and bεFp,E[r] is a set of rational points of a prime order r,φp is Frobenius endomorphism, andthe order r and a trace t of the Frobenius endomorphism φp 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; andcomputation means for performing pairing computation by using the rational function f′χ,Q(S) as Formula (1):e(Q,S)=ƒ′χ,Q(S)(pk−1)/r  (1).

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First Claim