Patent ID: 8718276

Claim:
Method of execution of a cryptographic calculation in an electronic component comprising a step of obtaining a point P(X,Y) from at least one parameter t, on an elliptical curve satisfying the equation: Y 2 =f ( X ); and starting from polynomials X 1 (t), X 2 (t), X 3 (t) and U(t) satisfying the following Skalba equality: f ( X 1 ( t ))· f ( X 2 ( t )· f ( X 3 ( t )= U ( t ) 2 in the finite field F q , regardless of the parameter t, q satisfying the equation q=3 mod 4; said method comprising the following steps: /1/ obtaining a value of the parameter t; /2/ determining the point P by executing the following substeps: /i/ calculating X 1 =X 1 (t), X 2 =X 2 (t), X 3 =X 3 (t) and U=U(t) and calculating a term f(X 1 )·f(X 2 ); /ii/ if the term f(X 1 )·f(X 2 ) is a squared term in the finite field F q then testing whether the term f(X 3 ) is a squared term in the finite field F q and calculating the square root of the term f(X 3 ), point P having X 3 as abscissa and the square root of the term f(X 3 ) as ordinate; /iii/ otherwise, testing whether the term f(X 1 ) is a squared term in the finite field F q and in this case, calculating the square root of the term f(X 1 ), point P having X 1 as abscissa and the square root of the term f(X 1 ) as ordinate; /iv/ otherwise, calculating the square root of the term f(X 2 ), point P having X 2 as abscissa and the square root of the term f(X 2 ) as ordinate; /3/ using said point P in a cryptographic application selected from the group consisting of encryption or hashing or signature or authentication or identification.