Countermeasure procedures in an electronic component implementing an elliptical curve type public key encryption algorithm

A countermeasure method in an electronic component implementing an elliptical curve type public key encryption algorithm, wherein a point P on the elliptical curve is represented by the projective coordinates (X, Y, Z) such that x=X/Z and y=Y/Z^3, x and y being the coordinates of the point on the elliptical curve in terms of affine coordinates, said curve comprising n elements and being defined on a finite field GF(p), where p is a prime number and the curve has the equation y^2=x^3+a*x+b, or defined on a finite field GF(2^n), with the curve having the equation y^2+x*y=x^3+a*x^2+b, where a and b are integer parameters, the method comprising the steps of:

• 1) Drawing at random an integer λ such that 0<λ<p;
• 2) For a point P represented by projective coordinates (X1, Y1, Z1), calculating X′1=λ^2*X1, Y′1=λ^3*Y1 and Z′1=λ*Z1, to define the coordinates of the point P′=(X′1, Y′1, Z′1);
• 3) Calculating an output point Q=2*P′ that is represented by projective coordinates (X2, Y2, Z2);
• and
• 4) Performing a public key cryptographic operation using a key which is based upon the value Q.