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 said public key, and calculating a private exponent d for said private key from said public exponent and said 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 comprises a step: of checking to check that λ(n)=0 mod (p-1) and λ(n)=0 mod (q-1).