1. A method, performed by a processor of a cryptographic system, of cryptographically processing a message, using encryption and/or digital signature mechanisms based on public and private cryptographic key pairs in the additive group of integers modulo n, with n being the product of two prime numbers p and q, the method comprising: verifying the integrity of the public and private cryptographic key pairs; and encrypting and/or digitally signing the message using the public and private cryptographic key pairs, wherein the step of verifying of the integrity of the public and private cryptographic key pairs comprises the steps of computing, on the basis of said number n, a public exponent e of said public key, and of a private exponent d of said private key, of two candidate factors p′ and q′ corresponding respectively to the numbers p and q, and verifying a consistency of said private exponent with respect to said public exponent and to said number n, said verification step involving said candidate factors.