| 摘要 |
PROBLEM TO BE SOLVED: To provide a method, a device, and a program for determining elements on a partial group capable of constituting a one-way function that can result in the difficulty of an elliptic DH determination problem. SOLUTION: In a temporary storage means, tE*μ<SB>L</SB>(μ<SB>L</SB>is a multiplicative group formed of the L-th root of multiplicative identity 1 on an algebraically closed field of a definition body K of an elliptic curve) is stored in advance. In an input means, points R<SB>1</SB>, R<SB>2</SB>E*E[L] (R<SB>1</SB>≠O) (O has a property of being O+R<SB>1</SB>=R<SB>1</SB>with respect to an arbitrary point R<SB>1</SB>on E[L]) on E[L] (a linear space on Z/LZ wherein elliptic addition is addition and elliptic scalar multiple is scalar multiple) are inputted. In a pairing means, pairing e<SB>L</SB>(R<SB>1</SB>, R<SB>2</SB>) is calculated, and the calculation result t is stored in the temporary storage means. In an output means, "true" is outputted when t=1, and "false" is outputted when t≠1. E* in the above is a set symbol meaning "belong to". COPYRIGHT: (C)2009,JPO&INPIT
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