| 摘要 |
Generation of a message m of order λ(n) for a test of the integrity of the generation of a pair of cryptographic keys within the multiplicative group of integers modulo n=p·q, including: —key pair generation including, to generate p and q: a random selection of candidate integers; and a primality test; —a first search of the multiplicative group of integers modulo p for a generator a; —a second search of the multiplicative group of integers modulo q for a generator b; —a third search for a number y, as message m, verifying: 1≦γ≦n−1, where γ=a mod p and γ=b mod q, the first or second search being performed during the primality test. |
| 主权项 |
1. A method of generating a message m of order λ(n), λ(n) being the lowest common multiple between p−1 and q−1, p and q being two prime numbers, for its use in a test of the integrity of generation of a pair of public and private cryptographic keys in the multiplicative group of integers modulo n, with n being the product of the two prime numbers p and q, the method including:
a step of generation of said pair of public and private cryptographic keys, said step including, for generating the numbers p and q:
a random drawing (200, 202) of candidate integers, anda test (201, 203) of the primality of said candidate integers, a first step (304) of searching for a generator a of the multiplicative group of integers modulo p, zero being excluded, a second step (304) of searching for a generator b of the multiplicative group of integers modulo q, zero being excluded, a third step (205) of searching for a number γ, as message m, satisfying: 1≦γ≦n−1 with γ=a mod p and y=b mod q,wherein at least one of said first and second search steps is executed during said primality test. |
