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.