Secure method for reconstructing a reference measurement of a confidential datum on the basis of a noisy measurement of this datum, notably for the generation of cryptographic keys

A method for enrolling a reference datum w having n digits, executed by a calculation unit, said method comprising at least the following steps:

• for the enrolling, selecting an error correcting code C of a length L greater than n, the correction capacity of the error correcting code being greater than the expected number of errors between two acquisitions of the reference datum w, the correcting code having a predetermined minimum dimension corresponding to a minimum security level;
• generating an extended datum we by increasing the size of the reference datum w with L-n digits making up a secret key Sk;
• randomly choosing a word c of the selected error correcting code C;
• combining the said word c with the said extended datum we, so as to generate a datum s for reconstructing we;
• recording the datum s on a storage medium;
• and
• for reconstructing an extended reference datum we having L digits on the basis of a noisy datum w′ having n digits, n≦L;
• and of a reconstruction datum s generated during the enrolling of the reference datum w, the reconstructing comprising:
• generating an extended noisy datum we′ by increasing the size of the noisy datum w′ with L-n digits making up the said key Sk,
• combining the reconstruction datum s with the extended noisy datum we′ to obtain a word c′ of length L,
• decoding the word c′ as word c″ belonging to the code C, and
• combining the word c″ with the reconstruction datum s to generate a stabilized datum ws equal to the extended reference datum we if the word c″ obtained by decoding is identical to the word c.