WHITE-BOX PROTECTION FOR CRYPTOGRAPHIC ALGORITHMS INCLUDING CALCULATION OF A QUADRATIC FORM

摘要

The invention relates to a method for implementing a cryptographic algorithm including a calculation step for a quadratic form Y = A(x1,...,xn ) = (I), where the n > 1 variables x1,..., xn as well as the coefficients a(ij) belong to a finite body K of q elements, and where Y is the value taken by the quadratic form A(x1,...,xn) for a given value of variables x1,...,xn. Said calculation step is performed by means of the following sub-steps: determining, as a function of the parity of q and n, a canonical quadratic form Y = C(X1,...,Xn) equivalent to said form A(x 1,...,xn ), and of the change in linear variable X = Lx associated with this placing in canonical form; calculating the value of transformed variables X1,...,Xn associated with the value of variables x1,...,xn ; subdividing all of the terms of said canonical quadratic form C(X1,..., Xn) in sub-assemblies each including one or more of these terms; calculate, for each of said sub-assemblies, the respective total of the terms of the sub-assembly, said calculation being performed, for at least one of the sub-assemblies, by means of a table of values; and summation of said respective sums to obtain said value Y taken by the quadratic form.