| 摘要 |
PROBLEM 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. SOLUTION: The multi-pairing operation method for outputting the product of elementsΠ<SP>e</SP>(P<SB>i</SB>, Q<SB>i</SB>) on a plurality of finite bodies GF(p<SP>k</SP>) is provided. When the result of assigning the above set of inputs (P<SB>i</SB>, Q<SB>i</SB>) to a rational function f<SB>p</SB>satisfying (f<SB>p</SB>)=m(P)-m(O) is defined as F<SB>i</SB>,ΠF<SB>i</SB>is directly obtained by the operation to evaluate a divisor rational expression without calculating the individual F<SB>i</SB>. Also, the pairing comparison method for judging whether the pairing results e(P<SB>1</SB>, Q<SB>1</SB>) and e(P<SB>2</SB>, Q<SB>2</SB>) are equal is provided. In this method, the multi-pairing operation is performed wherein (P<SB>1</SB>, Q<SB>1</SB>) and (P<SB>2</SB>, -Q<SB>2</SB>) are set as inputs and the product e(P<SB>1</SB>, Q<SB>1</SB>)×e(P<SB>2</SB>, -Q<SB>2</SB>) is outputted. By comparing the result of the multi-pairing with 1, the correctness of the pairing result is confirmed. COPYRIGHT: (C)2007,JPO&INPIT
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