Method and device for reducing a polynomial in a binary finite field, in particular for a cryptographic application.

摘要

Usable process in a cryptographic process in an electronic device for reducing a first word of binary data corresponding to a polynomial C (x) and having a maximum length of 2n-1 to a second data word having a maximum length equal am which corresponds to a polynomial C''0 (x) equivalent to C (x) in a binary finite field GF (2m) elements which have a maximum length equal to m being less than or equal to n m, which includes the following steps: - preparing a reduction polynomial R (x) consisting of a trinomial or pentanomio; - partitioning the first data word in a first subword binary data C0 and a second subword binary data C1 whose corresponding polynomials C0 (x) and C1 (x), satisfying the equation C (x) = C1 (x) * xm + C0 (x), and making the second sub-word data to form a first addend; - right shift of the second sub-word data to form a second term summand, and repeating step shift to the right to form other terms addends until each term not disappear polynomial reduction than the xm term, I have assigned a term of summands, the width of each step of right shift equal to the difference between m and the order of a corresponding term does not disappear reduction polynomial; - adding the addend terms formed to the first subword data to form a data word sum; - if the data word sum thus determined has a length greater than m, applying the process steps from the partitioning step to the data word addends formed until the data word sum thus determined has a amy maximum length equal therefore constitutes the second data word.