Countermeasure method in an electric component implementing an elliptical curve type public key cryptography algorithm

1. A countermeasure method in an electronic component implementing a public key cryptography algorithm based on the use of elliptical curves in which a deciphering integer d′ is calculated, using a private key d and a number of points n on an elliptical curve, such that the deciphering of any enciphered message, by means of a deciphering algorithm, with d′, gives the same result as with d, by effecting the operation Q=d*P, where P is a point on the curve, said method including the following steps:

1) determining a security parameter s;

2) drawing a random number k between 0 and 2 s ;

3) calculating the integer d′=d+k*n; and

4) calculating Q=d′*P.

2. A countermeasure method according to claim 1 , wherein a new deciphering integer d′ is calculated at each new execution of the deciphering algorithm.

3. A countermeasure method according to claim 1 , further including the step of incrementing a counter at each new execution of the deciphering algorithm until a fixed value T is reached.

4. A countermeasure method according to claim 3 , wherein, once the value T has been reached, a new deciphering integer is calculated and the counter is reset to zero.

5. A countermeasure method according to claim 3 , wherein the value T is equal to the integer 16.

6. A countermeasure method in an electronic component implementing a public key cryptography algorithm based on the use of elliptical curves defined on a finite field GF(p), where p is a prime number, according to the equation y 2 =x 3 +ax+b and where a random calculation modulus of the form p′=p*r, where r is a random integer, is used at each new execution of the algorithm, said method including the execution of a scalar multiplication operation according to the following steps:

1) determining a security parameter s;

2) drawing a random number r whose binary representation comprises s bits;

3) calculating p′=p*r;

4) executing the scalar multiplication operation Q=d.P, where P is a point on a curve, and said operation is performed modulo p′; and

5) performing the reduction operation modulo p of the coordinates of the point Q.

7. A countermeasure method according to claim 6 , wherein a new integer is calculated at each new execution of the cryptography algorithm.

8. A countermeasure method according to claim 6 , further including the step of incrementing a counter at each new execution of the cryptography algorithm.

9. A countermeasure method according to claim 8 , wherein the counter is reset to zero when it has reached a value T.

10. A countermeasure method according to claim 9 , wherein the value T is equal to sixteen.

11. A countermeasure method in an electronic component implementing a public key cryptography algorithm based on the use of elliptical curves in which a new deciphering key d′ is calculated, using the private key d and a number of points n on an elliptical curve, such that the deciphering of any enciphered message, by means of a deciphering algorithm, with d′, gives the same result as with d, by performing the operation Q=d*P, where P is a point on the curve to which a scalar multiplication algorithm is applied, said method comprising the following steps:

1) drawing a random point R on the curve;

2) calculating P′=P+R;

3) performing the scalar multiplication operation Q′=d.P′;

4) performing the scalar multiplication operation S=d.R; and

5) calculating Q=Q′−S.

12. A countermeasure method according to claim 11 , further including the step of incrementing a counter at each new execution of the deciphering algorithm up to a value T.

13. A countermeasure method according to claim 12 , wherein the counter is reset to zero once the value T has been reached.

14. A countermeasure method according to claim 11 , wherein the elliptical curve has two points such that S=d*R, and wherein steps 1 and 4 are replaced by the following steps 1′ and 4′:

1′) Replacing R with 2.R;

4′) Replacing S with 2.S.

15. A countermeasure method according to claim 14 , further including the step of incrementing a counter at each new execution of the deciphering algorithm up to a value T.