Cryptographic apparatus such as a smart card with implementation of point multiplication on elliptical curves resistant to side channel effects

摘要

The apparatus such as a smart card with a processor and memory area is configured such that when a point multiplication is carried out on an elliptical curve with a whole number, the following operations are undertaken: The multiplier is represented in the form of a sum based on whole numbers and the number of whole numbers used. Randomly selected points are arranged on the curve. The points are selected such that no point is infinite. Operations are carried out which modify the value of variables dependent on the number of whole numbers and the sum of points is added to each variable. The sum is calculated using the modified values of the variables.