| 摘要 |
PROBLEM TO BE SOLVED: To provide an expression conversion technique enabling conversion to projection expression expressing an algebraic torus T<SB>2</SB>(F<SB>q^r</SB>) from affine expression expressing an algebraic torus T<SB>2r</SB>(F<SB>q</SB>) even when prime factor order exists and reducing processing load of operation processing after conversion. SOLUTION: An obtaining part 101 obtains an origin (c<SB>0</SB>, c<SB>1</SB>) expressed in affine expression on an algebraic torus T<SB>6</SB>(F<SB>p^r</SB>), system parameters w for determining polynomial of secondary extension, and a system parameter δ for determining polynomial of tertiary extension. A multiplying part 102 carries out a multiplication determined by a condition in which the origin of (c<SB>0</SB>, c<SB>1</SB>) is included in the algebraic torus T<SB>2r</SB>(F<SB>q</SB>) by using (c<SB>0</SB>, c<SB>1</SB>), w, δ, and polynomial of secondary extension and base and polynomial of tertiary extension and base. An addition and subtraction part 103 carries out addition by using a result of multiplication by the multiplying part 102. An output part 104 outputs the origin expressed in projection expression of the algebraic torus T<SB>2</SB>(F<SB>q^r</SB>). COPYRIGHT: (C)2010,JPO&INPIT
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