COMPUTING DEVICE AND METHOD, AND PROGRAM

PROBLEM TO BE SOLVED: To provide a computing technique for performing square computation on a finite field at high speed. SOLUTION: Elements of a finite field are input into an input unit 101 in vector representation. A square computation rule creation unit creates a square computation rule which is defined by a fixed modulus polynomial and a basis and in which a first conditional expression and a second conditional expression are applied to Karatsuba-algorithm. The first conditional expression is based on a first property that the elements of a sixth degree extension field Fq^6 are the elements of T2(Fq^r). The second conditional expression is based on a second property that the elements of the sixth degree extension field Fq^6 are the elements of T2r(Fq). A multiplication unit 102 performs multiplication according to the square computation rule. An addition/subtraction unit 103 calculates each element included in the vector representing the results of square computation by performing addition/subtraction using the multiplication results of the multiplication unit 102 and the elements of vector according to the square computation rule. An output unit 104 outputs the results of computation by the addition/subtraction unit 103 as the results of square computation. COPYRIGHT: (C)2010,JPO&INPIT