Pairing arithmetic device, pairing arithmetic method and recording medium having pairing arithmetic program recorded thereon
A pairing arithmetic device is provided with aCPU whichcalculates pairing e(S,Q), with F as a rational function calculated using S∈G1, Q∈G2, a predeterminedinteger variable as χ, and an algorithm (MMA) of a mirror with respectto multi-pairing as F. The order r, the trace t of the Frobenius endomorphism map/image Φp are specifiedusing the integer variable χ according to the degree of embedding k. The CPU carries out the arithmetic operation by means of: an inputting means which inputs the aforementioned integervariable χ, the rational pointS, and the rational point Q into their respective predeterminedregisters; a calculating means which calculates F; a calculating means which calculates values at a rational point Q(xQ,yQ) on a straight line which passes through predeterminedrational points; a calculating means which calculates fχ,s(Q) using Fand the aforementioned value; and a calculating means which uses fχ,s(Q)to calculate the pairing e(S,Q) as a [83].
United States
US8477934
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