Patent ID: 8379844

Claim:
A method, for being performed by a computer system, of obtaining an Elliptic Curve Scalar Multiplication (ECSM) product of a scalar and a base point on an elliptic curve in a manner that counters power analysis attacks, said base point having a prime order, said method comprising: receiving said base point, said scalar and a previous set of parameters used to split said scalar for a previous ECSM, said previous set of parameters including a previous quotient and a previous remainder determined using said scalar as a dividend and a first random integer as a divisor; selecting a second random integer; determining a new set of parameters for splitting said scalar, said determining based on said previous set of parameters and said second random integer, said new set of parameters including a successive quotient and a successive remainder, said determining said new set of parameters including: determining said successive quotient based on said previous quotient, said previous remainder and said second random integer; and determining said successive remainder based on said previous quotient, said previous remainder and said second random integer, said determining said successive remainder including: determining a temporary sum of said previous quotient and said second random integer; determining a temporary product of said temporary sum and said first random integer; determining a representation of said temporary product modulo said second random integer; and determining said successive remainder as a sum of said previous remainder and said representation; and obtaining said ECSM product using said new set of parameters to split said scalar.