MULTI-PAIRING OPERATION METHOD, PAIRING COMPARISON METHOD, DEVICE AND PROGRAM USING THEM

摘要

PPROBLEM TO BE SOLVED: To attain the high speed of a multi-pairing method and a paring comparison method by reducing operation amount of multi-pairing of an elliptic curve. PSOLUTION: The multi-pairing operation method for outputting the product of elements ΠSPe/SP(PSBi/SB, QSBi/SB) on a plurality of finite bodies GF(pSPk/SP) is provided. When the result of assigning the above set of inputs (PSBi/SB, QSBi/SB) to a rational function fSBp/SBsatisfying (fSBp/SB)=m(P)-m(O) is defined as FSBi/SB, ΠFSBi/SBis directly obtained by the operation to evaluate a divisor rational expression without calculating the individual FSBi/SB. Also, the pairing comparison method for judging whether the pairing results e(PSB1/SB, QSB1/SB) and e(PSB2/SB, QSB2/SB) are equal is provided. In this method, the multi-pairing operation is performed wherein (PSB1/SB, QSB1/SB) and (PSB2/SB, -QSB2/SB) are set as inputs and the product e(PSB1/SB, QSB1/SB)×e(PSB2/SB, -QSB2/SB) is outputted. By comparing the result of the multi-pairing with 1, the correctness of the pairing result is confirmed. PCOPYRIGHT: (C)2007,JPO&INPIT