Method of verifying integrity of a pair of cryptographic keys and cryptographic device

A verification method of verifying integrity of a pair of public and private keys within a group of integers, the groups of integers being an additive group of integers modulo N, with N being the product of two primary numbers p and q, the method comprising:

• calculating an exponent that is a candidate private exponent d′ corresponding to an exponent d, the exponent d being a private exponent of said private key;
• executing a test of integrity comprising
• processing an initial test data value using one of:
• (i) a public exponent e of the public key and (ii) the candidate private exponent d′ to obtain a first result,
• processing the first result using the other of:
• (i) the public exponent e of the public key and (ii) the candidate private exponent d′ to obtain a second result,
• comparing the initial test data value with the second result, and
• verifying coherence of the candidate private exponent d′ with respect to the public exponent e of said public key and the numbers p and q, the verifying using
• a first multiple of the public exponent e of the public key, the first multiple being modulo (p−1), and
• a second multiple of the public exponent e of the public key, the second multiple being modulo (q−1);
• and
• determining, using the first multiple of the public exponent e of the public key and the second multiple of the public exponent e of the public key, that the pair formed with the public key and the private key having the candidate private exponent d′ is corrupted.