Method for performing a cryptographic task in an electronic hardware component

1. A method for performing a cryptographic task on at least one numerical datum, said method comprising:

a step of at least partial use of a cryptographic function in an electronic hardware component as an asymmetric cryptographic public key, wherein the cryptographic function comprises a basic encryption function obtained by the addition between:

an intermediate function derived from composition of an error-correcting coding function with a first function, wherein the first function is a polynomial function of degree d f greater than or equal to two,

and a second function, wherein the second function is a polynomial function of degree d E greater than or equal to two;

a step of converting between the at least one numeric datum and at least one encrypted numeric datum by applying the cryptographic function.

2. The method for performing a cryptographic task as claimed in claim 1 , wherein the cryptographic function comprises an improved encryption function obtained by composition of a concealment function with said basic encryption function.

3. The method for performing a cryptographic task as claimed in claim 1 , wherein the degree d f of the first polynomial function and the degree d E of the second polynomial function have the same value.

4. The method for performing a cryptographic task as claimed in claim 1 , wherein the intermediate function and the second function have the same expansion.

5. The method for performing a cryptographic task as claimed in claim 1 , wherein the second function comprises a multiplication of a plurality of linear functions.

6. The method for performing a cryptographic task as claimed in claim 1 , in which the cryptographic task comprises an encryption of the at least one datum, and wherein said step of converting comprises a step of encrypting the at least one numeric datum into the at least one encrypted numeric datum by said encryption function.

7. The method for performing a cryptographic task as claimed in claim 1 , in which the cryptographic task comprises a decryption of the at least one encrypted numeric datum, and wherein said step of converting comprises the following steps:

decoding the at least one encrypted numeric datum into at least one intermediate datum by way of a decoding function associated with the error-correcting coding function; and

applying an inverse function of the first function to the at least one intermediate datum so as to obtain at least one decrypted datum.

8. The method for performing a cryptographic task as claimed in claim 1 , in which the task comprises a decryption of the at least one encrypted numeric datum, and wherein said step of converting comprises the following steps:

obtaining at least one intermediate datum by application of a decoding function, associated with the error-correcting coding function, to the at least one encrypted numeric datum;

applying the inverse function of the second function to the at least one intermediate datum so as to obtain at least one decrypted datum.

9. The method for performing a cryptographic task as claimed in claim 1 , in which the task comprises a decryption of the at least one encrypted numeric datum, which comprises the following steps:

determination, by application of a decoding function, associated with the error-correcting coding function, to the at least one encrypted numeric datum, of a plurality of potential pairs of elements;

selection of a new pair of elements from among said plurality of potential pairs;

computation of a candidate datum by application of an inverse function of the second function to the second element of the selected potential pair;

computation of an intermediate datum by application of the first function to the candidate datum;

comparison of the first element of the selected pair with the intermediate datum;

if the first element and the intermediate datum are identical, determination of at least one decrypted datum on the basis of the candidate datum;

if the first element and the intermediate datum are different, return to the step of selection for selection of a new pair of elements from among said plurality of potential pairs.

10. The method for performing a decryption of an encrypted datum as claimed in claim 7 , wherein the method comprises a preliminary step of applying an inverse function of a concealment function to an improved encrypted datum so as to obtain a basic encrypted datum to be decrypted.

11. The method for performing a cryptographic task as claimed in claim 7 , in which the task comprises an authentication, by a first entity, of an encrypted message sent by a second entity.

12. A method for generating an asymmetric cryptography public key, comprising the following steps:

composition of a first function with an error-correcting coding function so as to obtain an intermediate function, wherein the first function is a polynomial function of degree d f greater than or equal to two;

addition of a second function to said intermediate function with an electronic hardware component so as to obtain a basic public encryption function usable as the asymmetric cryptographic public key, wherein the second function is a polynomial function of degree d E greater than or equal to two; and

transmitting the asymmetric cryptographic public key from the electronic hardware component to another entity.

13. The method of claim 12 and further comprising fabricating an advanced asymmetric cryptography public key, wherein fabricating comprises:

a step of composition of a concealment function with the basic public encryption function obtained by the step of addition.

14. A cryptographic device comprising:

an electronic hardware device comprising a computation module configured to use a cryptographic function as an asymmetric cryptographic public key, which comprises a basic encryption function obtained by the addition between:

an intermediate function derived from composition of an error-correcting coding function with a first function, wherein the first function is a polynomial function of degree d f greater than or equal to two; and

a second function, wherein the second function is a polynomial function of degree d E greater than or equal to two; and

wherein the computation module is further configured to convert between the at least one numeric datum and at least one encrypted numeric datum by applying the cryptographic function.

15. The method for performing a decryption of an encrypted datum as claimed in claim 8 , wherein the method comprises a preliminary step of applying an inverse function of a concealment function to an improved encrypted datum so as to obtain a basic encrypted datum to be decrypted.

16. The method for performing a decryption of an encrypted datum as claimed in claim 9 , wherein the method comprises a preliminary step of applying an inverse function of a concealment function to an improved encrypted datum so as to obtain a basic encrypted datum to be decrypted.

17. The method for performing a cryptographic task as claimed in claim 8 , in which the task comprises an authentication, by a first entity, of an encrypted message sent by a second entity.

18. The method for performing a cryptographic task as claimed in claim 9 , in which the task comprises an authentication, by a first entity, of an encrypted message sent by a second entity.

19. The method for performing a cryptographic task as claimed in claim 10 , in which the task comprises an authentication, by a first entity, of an encrypted message sent by a second entity.