EXTENSION FIELD SQUARE ROOT CALCULATION APPARATUS, EXTENSION FIELD SQUARE ROOT CALCULATION METHOD, EXTENSION FIELD SQUARE ROOT CALCULATION PROGRAM, AND RECORDING MEDIUM WITH ITS PROGRAM RECORDED

摘要

PROBLEM TO BE SOLVED: To provide an extension field square root calculation technique that realizes reduced processing cost of finding on GF(q^m) the square roots of an element on GF(q^m).;SOLUTION: When finding on GF(q^m) the square roots x of an element y on GF(q^m), a qⁿ-power Frobenius mapping processing technique is used in finding the square roots x. The qⁿ-power Frobenius mapping processing technique can produce a vector representing x^q only by multiplying a vector (x_i) representing that x is an element of the set GF(q^m) with a matrix (c_ij). The processing cost is generally the same as that of a single multiplication on GF(q^m). The processing cost of finding on GF(q^m) the square roots of an element on GF(q^m) can be thus significantly reduced.;COPYRIGHT: (C)2005,JPO&NCIPI