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

摘要

When converting an affine representation representing a 2r-th degree algebraic torus T_2r(F_q) (r is a prime number, and q is an integer) to a projective representation representing a quadratic algebraic torus T₂(F_q̂r), a representation converting apparatus acquires member (c₀,c₁, . . . ,c_r−2), (c_i is a member of a finite field F_q, where 0≦i≦r−2) of a 2r-th degree algebraic torus T_2r(F_q) represented by the affine representation. The apparatus performs a multiplication operation on the acquired member. The multiplication operation is determined by a condition under which a member of a quadratic algebraic torus T₂(F_q̂r) is included in the 2r-th degree algebraic torus T_2r(F_q), a modulus and a base of a quadratic extension, and a modulus and a base of an r-th degree extension. The representation converting apparatus then performs an addition and subtraction operation determined by the condition, the moduli, and the bases.