Integrity verification of cryptographic key pairs
Method of integrity verification of 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 including the following steps: of computation ( 201 ), on the basis of the number n, of a public exponent e of the public key, and of a private exponent d of the private key, of two candidate factors p′ and q′ corresponding respectively to the numbers p and q, of verification ( 206 ) so as to verify the consistency of the private exponent with respect to the public exponent and to the number n, the verification step involving the candidate factors.
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.
2. The method according to claim 1 , wherein said verification step pertains to the product of the public exponent e and of said private exponent d.
3. The method according to claim 2 , wherein during said verification step, it is verified whether the product of the public exponent e and of said private exponent d is congruent to 1 modulo λ′(n), the least common multiple between (p′−1) and (q′−1).
4. The method according to claim 2 , wherein during said verification step, it is verified whether the product of the public exponent e and of said private exponent d is congruent to 1 modulo the product (p′−1)·(q′−1).
5. The method according to claim 1 , wherein said verification step pertains to the least common multiple λ(n) between (p−1) and (q−1).
6. The method according to claim 5 , wherein during said verification step, the least common multiple λ(n) between (p−1) and (q−1) is compared with the least common multiple λ′(n) between (p′−1) and (q′−1).
7. The method according to claim 5 , wherein during said verification step, it is verified whether:
the least common multiple λ(n) between (p−1) and (q−1) is congruent to 0 modulo (p′−1), and
the least common multiple λ(n) between (p−1) and (q−1) is congruent to 0 modulo (q′−1).
8. The method according to claim 1 , wherein said candidate factors are computed by a probabilistic factorization algorithm.
9. A computer program encoded on a non-transitory computer-readable medium, comprising instructions that, upon being loaded and executed by a processor of a cryptography device, causes the cryptography device to implement the method according to claim 1 .
10. A cryptographic device comprising a microprocessor configured to implement the method according to claim 1 .
11. The cryptographic device according to claim 10 , wherein the cryptographic device is portable.