Method of evaluating a function and associated device
AssigneeOberthur Technologies
InventorsEmmanuel Prouff, Matthieu Rivain
Life of this patent
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Abstract
A method for evaluating a function of a finite field of characteristic p into itself, for an element x of the field, uses an evaluation, for the element x, of a polynomial formed by a plurality of monomials. The evaluation of the polynomial includes the following steps: determining monomials the degree of which is an integer power of the characteristic p by successive raisings of the element x to the power p; and determining monomials the degree of which is different from an integer power of the characteristic p on the basis of the determined monomials, the degree of which is an integer power of the characteristic p, and by at least one multiplication. An evaluating device is also provided.
Claims20
A method, implemented by an electronic circuit, for evaluating a function of a finite field of characteristic p into itself, for an element x of the field, said element x representing data masked by a masking operation, said function being non-linear with respect to said masking operation, the method comprising:
- an evaluation, for said element x, of a polynomial formed by a plurality of monomials, wherein the polynomial is formulated using successive decompositions of a polynomial interpolating said function, thereby reducing the degree of the polynomial used to evaluate the function
- wherein the evaluation of the polynomial thus formulated comprises the following steps:
- evaluating monomials the degree of which is an integer power of the characteristic p by means of successive raisings of the element x to the power p;
- obtaining monomials the degree of which is different from an integer power of the characteristic p on the basis of the evaluated monomials, the degree of which is an integer power of the characteristic p, and by means of at least one multiplication of the element x by one of said evaluated monomials the degree of which is an integer power of the characteristic p,
- wherein said evaluating the function maintains the masking.
A device for evaluating a function of a finite field of characteristic p into itself, for an element x of the field, with evaluation, for said element x, of a polynomial formed by a plurality of monomials,
- wherein:
- said element x represents data masked by a masking operation,
- said function is non-linear with respect to said masking operation, and
- the polynomial is formulated using successive decompositions of a polynomial interpolating said function, thereby reducing the degree of the polynomial;
- the device comprising:
- means for evaluating monomials the degree of which is an integer power of the characteristic p by means of successive raisings of the element x to the power p;
- means for obtaining monomials the degree of which is different from an integer power of the characteristic p on the basis of the evaluated monomials, the degree of which is an integer power of the characteristic p, and by means of at least one multiplication of the element x by one of said evaluated monomials the degree of which is an integer power of the characteristic p;
- wherein the masking is maintained when the function is evaluated.
Dependencies are inferred from the claim text.