Patent ID: 8391479

Claim:
A method, for being performed by a computer system, of publishing an Elliptic Curve scalar multiplication product of a scalar and a base point in a manner that counters side-channel attacks, said method comprising: selecting a random integer; determining a quotient key-splitting parameter and a remainder key-splitting parameter by performing an integer division operation with said scalar as dividend and said random integer as divisor; determining that at least one of said quotient key-splitting parameter and said remainder key-splitting parameter is even; selecting a further random integer; determining that both of said quotient key-splitting parameter and said remainder key-splitting parameter are odd; determining whether both said quotient key-splitting parameter and said remainder key-splitting parameter are odd, and if not repeating said selecting and said determining of said quotient key-splitting parameter and said remainder key-splitting parameter; determining an interim point as a product of said further random integer and said base point, wherein said determining said interim point includes performing a fixed-sequence windowing method that includes defining a first table, said first table including odd multiples of said base point; determining a sum of a first product and a second product, wherein factors of said first product include said quotient key-splitting parameter and said interim point and factors of said second product include said remainder key-splitting parameter and said base point, wherein said determining said sum includes performing an interleaving method combined with said fixed-sequence windowing method including defining a second table, said second table including odd multiples of said interim point; and publishing said sum as said product of said scalar and said base point.