| 摘要 |
PROBLEM TO BE SOLVED: To speed up the final exponentiation calculation in pairing calculations using a rational point of an elliptic curve defined on a finite field of a general characteristic. SOLUTION: A pairing calculation device 100 performs, on the basis of point data f calculated from input pairing object data P and Q, a final exponentiation processing to calculate the (2<SP>2m</SP>-1)(2<SP>m</SP>-2<SP>(m+1)/2</SP>+1)-th power of the point data f. In this final exponentiation processing, a pairing final exponentiation calculation control section 51 controls a 2<SP>m</SP>-th orderoperation executing section 64 and an F<SB>2</SB>m operation executing section 71 so as to calculate the inverse element B<SP>-1</SP>of a halfway result B on the basis of a relational expression of B<SP>-1</SP>=B^(2<SP>2m</SP>). Thus, the inverse element of the halfway result can be calculated without using an inverse element derivation algorithm which takes time. COPYRIGHT: (C)2009,JPO&INPIT
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