ARITHMETICAL DEVICE, ARITHMETICAL DEVICE ELLIPTICAL SCALAR MULTIPLICATION METHOD AND ELLIPTICAL SCALAR MULTIPLICATION PROGRAM, ARITHMETICAL DEVICE MULTIPLICATIVE OPERATION METHOD AND MULTIPLICATIVE OPERATION PROGRAM, AS WELL AS ARITHMETICAL DEVICE ZE

摘要

An elliptical scalar multiplication (kG) is processed in a fixed calculation time regardless of a random number (k), enabling the timing analysis of the elliptical scalar multiplication (kG) to be prevented. An initial setting unit (121) sets a specific point (G) on an elliptic curve to a scalar multiplication variable (R). A scalar multiplication unit (122) refers to a bit string of t bits that represent the random number (k) one bit at a time from the top level, sets the value obtained by multiplying the scalar multiplication variable (R) to a task variable (R) [0] for each string referred to one bit at a time, and sets the value, which has been obtained by adding the specific point (G) to the value of the task variable (R) [0], to a task variable (R) [1]. The scalar multiplication unit (122) sets the task variable (R) [0] to the scalar multiplication variable (R) if the value of the bit referred to is 0, and sets the task variable (R) [1] to the scalar multiplication variable (R) if the value of the bit referred to is 1. A scalar multiplication point output unit (123) subtracts a constant value (2tG) from the scalar multiplication variable (R), and outputs the value obtained by subtraction as a scalar multiplication point (kG).