Cryptographic algorithm fault protections
View Patent ↗The invention relates to a method for securing the execution of a cryptographic algorithm A against fault attacks. Given a cryptographic key KO and a message M, the cryptographic algorithm A is set to compute a value A(KO,M). Given a relationship R between A(KO,M) and A(f(K 0 ),g(M)), where f and g are two bijections, and where f is different from the identity function, the method comprises: a. computing the expected result A(KO,M) of the cryptographic algorithm b. computing a modified result A(f(K 0 ),g(M)), by applying the cryptographic algorithm A on a modified key f(K 0 ) and on a message g(M), c. checking whether the relationship R between the values A(KO,M) and A(f(K 0 ),g(M)) computed in the two preceding steps is verified d. detecting an attack if the relationship R is not verified. The invention also relates to a cryptographic device embodying the above method.
1. A method for operating a cryptographic device to secure a cryptographic algorithm A executing on the cryptographic device against fault attacks, wherein, given a cryptographic key KO and a message M, the cryptographic algorithm A is set to compute a value A(KO,M), and wherein, given a relationship R between A(KO,M) and A(f(K 0 ),g(M)), where f and g are two bijections, and where f is different from the identity function, the method comprises:
a. computing the expected result A(KO,M) of the cryptographic algorithm;
b. computing a modified result A(f(K 0 ),g(M)), by applying the cryptographic algorithm A on a modified key f(KO) and on a message g(M)
c. checking whether the relationship R between the values A(KO,M) and A(f(K 0 ),g(M)) computed in the two preceding steps is verified;
d. detecting an attack if the relationship R is not verified.
2. The method according to claim 1 , wherein the bijection f consists in inverting all bits of the key KO.
3. The method according to claim 1 or 2 , wherein the bijection g consists in inverting all bits of the message M.
4. The method according to claim 1 or 2 , wherein the relationship R consists in the fact that the each bit of the expected result A(KO,M) is the inverse of the corresponding bit of the modified result A(f(K 0 ),g(M)).
5. The method according to claim 1 or 2 , comprising generating n random keys K 1 . . . Kn, computing in random order A(Ki,M) and A(f(Ki),g(M)) for every i between 0 and n, checking the relationship R for each couple of values A(Ki,M) and A(f(Ki),g(M)), and detecting an attack if the relationship R is not verified for any i between 0 and n.
6. The cryptographic device implementing a cryptographic algorithm A, wherein, given a cryptographic key KO and a message M, the cryptographic algorithm A is set to compute a value A(KO,M), given a relationship R between A(KO,M) and A(f(K 0 ),g(M)), where f and g are two bijections, and where f is different from the identity function, the cryptographic device comprises means for:
a. computing the expected result A(KO,M) of the cryptographic algorithm;
b. computing a modified result A(f(K 0 ),g(M)), by applying the cryptographic algorithm A on a modified key f(KO) and on a message g(M);
c. checking whether the relationship R between the values A(KO,M) and A(f(K 0 ),g(M)) computed in the two preceding steps is verified;
d. detecting an attack if the relationship R is not verified.
7. The cryptographic device according to claim 6 , wherein the bijection f consists in inverting all bits of the key KO.
8. The cryptographic device according to claim 6 or 7 , wherein the bijection g consists in inverting all bits of the message M.
9. The cryptographic device according to claim 6 or 7 , wherein the relationship R consists in the fact that the each bit of the expected result A(KO,M) is the inverse of the corresponding bit of the modified result A(f(K 0 ),g(M)).
10. The cryptographic device according to claim 6 or 7 , comprising means for:
a. generating n random keys K 1 . . . Kn,
b. computing in random order A(Ki,M) and A(f(Ki),g(M)) for every i between 0 and n,
c. checking the relationship R for each couple of values A(Ki,M) and A(f(Ki),g(M)), and for
d. detecting an attack if the relationship R is not verified for any between 0 and n.
11. The cryptographic device according to claim 6 or 7 , wherein the cryptographic device is a smart card, a TPM, or an HSM.
12. The method according to claim 3 , wherein the relationship R consists in the fact that the each bit of the expected result A(KO,M) is the inverse of the corresponding bit of the modified result A(f(K 0 ),g(M)).
13. The method according to claim 3 , comprising generating n random keys K 1 . . . Kn, computing in random order A(Ki M) and A(f(Ki),g(M)) for every i between 0 and n, checking the relationship R for each couple of values A(Ki,M) and A(f(Ki),g(M)), and detecting an attack if the relationship R is not verified for any i between 0 and n.
14. The cryptographic device according to claim 8 , wherein the relationship R consists in the fact that the each bit of the expected result A(KO,M) is the inverse of the corresponding bit of the modified result A(f(K 0 ),g(M)).
15. The cryptographic device according claim 8 , comprising means for:
a. generating n random keys K 1 . . . Kn,
b. computing in random order A(Ki,M) and A(f(Ki),g(M)) for every i between 0 and n,
c. checking the relationship R for each couple of values A(Ki,M) and A(f(Ki),g(M)), and for
d. detecting an attack if the relationship R is not verified for any between 0 and n.
16. The cryptographic device according to claim 8 , wherein the cryptographic device is a smart card, a TPM, or an HSM.