Patent ID: 8913739

Claim:
A method, implemented by an integrated circuit (IC), for transforming data with a secret parameter in an elliptic curve cryptosystem based on an elliptic curve defined over an underlying prime field, comprising: multiplying, by the IC, a point of the elliptic curve, the point representing the data to be transformed, by a scalar representing the secret parameter, wherein the multiplying comprises performing at least one point addition operation and at least one point doubling operation on points of the elliptic curve, wherein the scalar is randomized by introducing thereto a random number, and a difference between the bit lengths of the scalar and the random number being greater than 2; providing, by the IC, a first representation, in affine coordinates, of the point of the elliptic curve to be multiplied and a second representation, in projective coordinates, of intermediate elliptic curve points obtained during the multiplying step; and performing, by the IC, the point addition operation in mixed coordinates using the first representation of the point of the elliptic curve by means of a first sequence of elementary prime field operations and the point doubling operation in the projective coordinates using the second representation of the intermediate elliptic curve points by means of a second sequence of elementary prime field operations, the first and second sequences having a same number of elementary prime field operations and each elementary prime field operation of the first sequence and a corresponding placed elementary prime field operation of the second sequence are of a same type, the elementary prime field operations of the first and second sequences comprising: a first type of prime field operations comprising field multiplication and field squaring of coordinates of the points of the elliptic curve; and a second type of prime field operations comprising field addition, field doubling, and field subtraction of coordinates of the points of the elliptic curve, wherein the first sequence of elementary prime field operations comprises at least two operations of the first type and at least two operations of the second type; and wherein: the field multiplication and the field squaring of coordinates of the points, when executed by the IC, take a same amount of operation time and consume a same amount of power by the IC; and the field addition, the field doubling, and the field subtraction of coordinates of the points, when executed by the IC, take a same amount of operation time and consume a same amount of power by the IC.