METHOD AND DEVICE FOR EXECUTING A CRYPTOGRAPHIC CALCULATION

1 . A method of generating a key for a cryptographic algorithm in an electronic component ( 21 );

according to which a prime number P is stored in memory in said electronic component;

said method comprising an operation of generating at least one secret prime number, said operation being carried out according to the following successive steps:

/a/ randomly selecting ( 11 ) two integers p 1 ′ and p 2 ′ whose sum is equal to a number p′;

/b/ deciding ( 12 ) whether said number p′ is a prime number, on the basis of a combining of the prime number stored in memory P with said numbers p 1 ′ and p 2 ′;

/c/ if it is decided that the number p′ is a prime number, storing (14) the numbers p 1 ′ and p 2 ′ in memory in the electronic component; otherwise repeating steps /a/ and /b/.

2 . The method as claimed in claim 1 , according to which a first integer p 1 and a second integer p 2 are determined so that the prime number P stored in memory is equal to the sum of said determined integers p 1 and p 2 ; and

according to which step /b/ is implemented on the basis of operations carried out on the numbers p 1 , p 2 , p 1 ′ and p 2 ′.

3 . The method as claimed in any one of the preceding claims, according to which the first and second integers p 1 and p 2 are determined in a random manner.

4 . The method as claimed in any one of the preceding claims, according to which step /b/ is carried out with the aid of a primality test based on combining a test of Solovay-Strassen type and a test of Miller-Rabin type.

5 . The method as claimed in any one of the preceding claims, furthermore comprising, before step /b/, the following step:

/a1/ verifying, on the basis of operations carried out on the numbers p 1 ′ and p 2 ′, that the number p′ is not divisible by one or more determined prime numbers; according to which steps /a/ and /a1/ are repeated if the number p′ is divisible by one of said determined prime numbers.

6 . The method as claimed in claim 5 , according to which step /a1/ comprises the following steps, for a determined prime number y strictly greater than 1:

randomly selecting a first number c and a second number d from among the integers ranging between 1 and y−1;

determining a number u according to the following equation:

u=c+dp 1 ′ modulo y;

determining a number v according to the following equation:

v=c−dp 2 ′ modulo y;

determining whether p is not divisible by y as a function of the difference between the number u and the number v.

7 . The method as claimed in any one of the preceding claims, according to which at least two prime numbers are generated by repeating steps /a/ to /c/ for construction of a pair of asymmetric keys.

8 . The method as claimed in any one of the preceding claims, according to which the cryptography algorithm is an algorithm of RSA type.

9 . An electronic component ( 21 ) for generating a key for a determined cryptographic algorithm;

said component comprising:

a selection unit ( 22 ) suitable for randomly selecting two integers p 1 ′ and p 2 ′ whose sum is a number p′;

a memory ( 23 ) for storing a prime number P and for storing the numbers p 1 ′ and p 2 ′ when it is decided that the sum of said numbers p 1 ′ and p 2 ′ is a prime number;

a decision unit ( 24 ) suitable for deciding whether the number p′ is a prime number on the basis of a combining of the prime number stored in memory P with said numbers p 1 ′ and p 2 ′.

10 . The electronic component as claimed in claim 9 , in which the selection unit ( 22 ) determines a first integer p 1 and a second integer p 2 so that the prime number P stored in memory ( 23 ) is equal to the sum of said determined integers p 1 and p 2 ; and in which the decision unit ( 23 ) decides whether the number p′ is an integer on the basis of operations carried out on the numbers p 1 , p 2 . p 1 ′ and p 2 ′.

11 . The electronic component as claimed in claim 10 , in which the selection unit ( 22 ) determines the first and second integers p 1 and p 2 in a random manner.

12 . The electronic component as claimed in any one of claims 9 to 11 , in which the decision unit ( 23 ) implements a primality test based on combining a test of Solovay-Strassen type and a test of Miller-Rabin type.

13 . The electronic component as claimed in any one of claims 9 to 12 , in which the selection unit ( 22 ) conducts a prior check, on the basis of operations carried out on the numbers p 1 ′ and p 2 ′, in order to verify that the number p′ is not divisible by one or more determined prime numbers; and

in which the selection unit ( 22 ) repeats the random selection of two integers p 1 ′ and p 2 ′ if p′ is divisible by a determined prime number.

14 . The electronic component as claimed in any one of claims 9 to 13 , in which the selection unit ( 22 ), in order to conduct the prior check in relation to a prime number y strictly greater than 1, furthermore comprises:

means designed to randomly select a first number c and a second number d from among the integers ranging between 1 and y−1;

means designed to determine a number u according to the following equation:

u=c+dp 1 ′ modulo y;

means designed to determine a number v according to the following equation:

v=c−dp 2 ′ modulo y;

means designed to determine whether p is not divisible by y as a function of the difference between the number u and the number v.

15 . The electronic component as claimed in any one of claims 9 to 14 , in which a plurality of prime numbers p′ is successively generated.

16 . The electronic component as claimed in any one of claims 9 to 15 , in which the cryptographic algorithm is an algorithm of RSA type.