| 摘要 |
PROBLEM TO BE SOLVED: To fast operate symmetric pairing on an extension field of a large characteristic.SOLUTION: In a pairing operation method, (p) is a prime factor which defines 6 as a divisor and is congruent with 5, (n) is an integer equal to or more than 1, and a condition of q=pis satisfied. Then, (b) is an element of a finite field F, Eis an elliptic curve of which the coefficient of a primary term on the finite field Fis 0 and of a constant term is (b), P:=(x, y),Q:=(x, y) is a point on the elliptic curve E, and both (x) and (y) coordinates x, yand x, yof the points P and Q are elements of the finite field F. Then, r' is a level number of the points P and Q, (u) is an element of a finite field F, u=bis satisfied, and ι is a map of transferring the point (x, y) to a point (ux, uy). A pairing operation device 1 comprises: a Miller operation section 12 which transfers a point Q to a point Q' in accordance with the map ι and computes a value (f) while computing x+xx+x; and an exponentiation arithmetic section 13 which computes (q-1)/r' power of the value (f) and outputs a value e(P, Q). |
