Patent ID: 7555122

Claim:
A cryptographic method for performing an elliptic curve point multiplication eP where e is an integer and P is a point on an elliptic curve for use in cryptographic processing device, comprising the following steps: representing the multiplier e in the form e = ∑ 0 ≤ i ≤ l ⁢ ⁢ b i ⁢ 2 wi using digits b i εB where w and l are integers and B is a set of integers; assigning randomly selected point representations to variables A b for at least one but not all bεB, such that none of the selected point representations is the point at infinity; assigning point representations to variables A b for all values of b for which randomly selected point representations were not assigned so that the sum ∑ b ∈ B ⁢ ⁢ b ⁢ ⁢ A b is the point at infinity; modifying the values of the variables A b in dependency of the digits b i such that the sum of the points 2 wi P over those indexes i for which b i =b holds is added to each variable A b ; and calculating the sum ∑ b ∈ B ⁢ ⁢ b ⁢ ⁢ A b by using the modified values of the variables A b .