REPRESENTATION CONVERTING APPARATUS, ARITHMETIC APPARATUS, REPRESENTATION CONVERTING METHOD, AND PROGRAM

摘要

PROBLEM TO BE SOLVED: To provide a representation converting technique which enables, even with the order being a prime number, conversion from an affine representation representing an algebraic torus T_2r(F_q) to a projective representation representing an algebraic torus T₂(F_q^r), and can reduce a processing load of arithmetic processes performed after the conversion.;SOLUTION: An acquiring unit 101 acquires: members (c₀, c₁) of an algebraic torus T₆(F_p^r) represented by an affine representation; a system parameter w that determines a modulus of a quadratic extension; and a system parameter δ that determines a modulus of a cubic extension. Using (c0, c1), w and δ, a multiplying unit 102 performs multiplication determined by: a condition under which the members (c₀, c₁) are included in an algebraic torus T_2r(F_q); the modulus and a base of the quadratic extension; and the modulus and a base of the cubic extension. An adding/subtracting unit 103 performs addition by use of a result of the multiplication performed by the multiplying unit 102. An output unit 104 outputs members of an algebraic torus T₂(F_q^r) represented by a projective representation.;COPYRIGHT: (C)2013,JPO&INPIT