Method for elliptic curve point multiplication
First Claim
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2. A mehtod for performing an elliptic curve point multiplication eP where is is an integer and P is a point on an elliptic curve for use in cryptography, comprising the following steps:
- representing the multiplier e in the form by using digits bi ∈
B where w and l are integers and B is a set of integers, assigning randomly selected point representations to variables Ab with b ∈
B where the points are chosen such that no Ab is the point at infinity, computing the sum and storing it in a variable Q;
performing operations that modify the values of the variables Ab in dependency of the digits bi such that the sum of the points 2wi P over those indexes i for which bi=b holds is added to each variable Ab;
calculating the sum by using the modified values of Ab, and subtracting from it the point stored in variable Q.
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Abstract
The method comprises three stages. In the first stage, randomly selected point representations are stored in variables. In the second stage, a right-to-left loop is executed that modifies the variable values in dependency of a multiplier. In the last stage, the result is calculated from the modified variable values.
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Citations
16 Claims
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2. A mehtod for performing an elliptic curve point multiplication eP where is is an integer and P is a point on an elliptic curve for use in cryptography, comprising the following steps:
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representing the multiplier e in the form by using digits bi ∈
B where w and l are integers and B is a set of integers,assigning randomly selected point representations to variables Ab with b ∈
B where the points are chosen such that no Ab is the point at infinity,computing the sum and storing it in a variable Q;
performing operations that modify the values of the variables Ab in dependency of the digits bi such that the sum of the points 2wi P over those indexes i for which bi=b holds is added to each variable Ab;
calculating the sum by using the modified values of Ab, and subtracting from it the point stored in variable Q. - View Dependent Claims (10, 14)
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3. A 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 cryptography, comprising the following steps:
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representing the multiplier e in the form using digits bi ⊂
B where w and l are integers and B is a set of integers,assigning randomly selected point representations to variables Ab is the point at infinity, but the sum is the point at infinity, where Bi denoted the set of absolute values of the integers in set B. perfoming operations that modify the values of the variables Ab in dependency of the digits bi such that the sum of the points 2wi P over those indexes i for which bi=b holds minus the sum of the points 2wi P over those negative indexes i for which bi -b holds is added to each variable Ab with b ∈
Bi;
calculating the sum by using the modified values of the variable Ab. - View Dependent Claims (6, 11, 15)
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4-1. The method according to claim 1, wherein in the third step the values 2wi P are computed in succession for i−
- O, . . . ,l and for each i the respective value is added to variable Abi.
Specification