Countermeasure method in an electric component implementing an elliptical curve type public key cryptography algorithm
AssigneeGemplus
InventorJean-Sébastien Coron
Life of this patent
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Abstract
A countermeasure method in an electronic component implementing an elliptical curve based public key cryptography algorithm. A new decryption integer d′ is calculated such that the decryption of an encrypted message on the basis of a private key d and the number of points n of an elliptical curve provides the same result with d′ as with d, by performing the operation Q=d*P, whereby P is a point of the curve. Four steps are employed in the calculation: 1) a security parameter s is determined, 2) a random number k ranging from 0-2s is drawn, 3) the integer d′=d+k*n is calculated, and 4) Q=d′.P is calculated.
Claims15
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 2s;
- 3) calculating the integer d′=d+k*n;
- and
- 4) calculating Q=d′*P.
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 y2=x3+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.
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.
Dependencies are inferred from the claim text.