Generation of cryptographic keys

Method for generating a pair of public and private cryptographic keys in the additive group of integers modulo n, where n is the product of two prime numbers p and q, the method including the following steps: calculating a public exponent e for the public key, and calculating a private exponent d for the private key from the public exponent and the public modulus, where d·e=1 mod λ(n), λ(n) being the least common multiple between p-1 and q-1, characterized in that the method furthermore includes a step: of checking to check that λ(n)=0 mod (p-1) and λ(n)=0 mod (q-1).