| 摘要 |
PROBLEM TO BE SOLVED: To speed up public key encipherment, the safety of which is grounded in the difficulty of the discrete logarithmic problem by speeding up a Jacobian group operation on a Cab curve. SOLUTION: With a frame work (refer to the figure) for a Jcobian group operation algorithm concerning a GPS curve presented by Galbraith and his set (a hyperelliptic curve is a special case of a GPS curve, and a GPS curve is a special case of a Cab curve), Step 2 and Step 3 are improved. In a calculation of an inverse ideal at Step 2, the method used for obtaining an inverse ideal of a numerical body is applied to this problem. At Step 3, calculation complexity of the algorithm is reduced in order by removing processing for solving unnecessary linear equations, using the relation that the two parameters a, b to be used for defining the Cab curve are prime to each other.
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