| 摘要 |
<P>PROBLEM TO BE SOLVED: To perform remainder calculation by polynomial used for extension first at high speed when power calculation on synthesized several-order extension field by extending a finite field by each polynomial. Ž<P>SOLUTION: In synthesized several-order extension field GF(p<SP>ml</SP>) being a finite field constituted by extending gradually a primary field GF(p) by m-th-order polynomial F(x) and first-order polynomial G(x), calculation of Q=Q2 mod F'(x)G(x) and Q=P×Q mod F'(x)G(x) based on polynomial F'(x) having less terms other than zero than terms of other than zero of m-th-order polynomial F(x) is performed, at the last, calculation of Q=Q mod F(x)G(x) is performed. Thus, half way remainder calculation is performed at high speed based on the polynomial F'(x) being less terms than the original F(x), at the last, reminder calculation is performed based on the original F(x). Ž<P>COPYRIGHT: (C)2010,JPO&INPIT Ž
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