| 摘要 |
The invention relates to a method for multiplication of a number with a point on an elliptical curve y<2> = x<3> + a * x + b, within a cryptographic algorithm, whereby x is a first co-ordinate of the elliptical curve, y is a second co-ordinate of the elliptical curve and the third elliptical curve is defined by a body with a characteristic greater than 3. According to the invention, an iterative algorithm is applied, in which one position of the number is sequentially processed after the other. When the position of the number is = 1, a first updated auxiliary point equal to double the original first auxiliary point is applied and a second updated auxiliary point the same as the sum of the original first and original second auxiliary points is applied (22) and, should the position of the number comprise a 1 (14), the first updated auxiliary point, the same as the sum of the original first and the original second auxiliary point is applied (16) and the updated second auxiliary point the same as double the original second auxiliary point is applied (18). After an iterative processing of all the points of the numbers (24, 26) the updated first auxiliary point represents the result (28) of the multiplication operation on the elliptical curve (10). In order to calculate the first and the second auxiliary point, efficient, explicit addition or multiplication formulae are given, which may be implemented in parallel such as to provide an efficient algorithm with a homogeneous flow profile and a homogeneous capacity profile which does not depend on the number, which is typically a secret code and thus to be protected from external access.
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