Verification process of authentication or biometric identification

A method for processing biometric data, comprising verification of the result of calculation of distance between a biometric candidate datum (a) and at least one biometric reference datum (b) each comprising a number n of indexed components (ai, bi), said calculation of distance comprising that of a polynomial of the components of the biometric data,

• the method being executed by a proving entity (P) and a verification entity (V), each entity being a processing unit comprising processing and communication means with the other entity, the method comprising steps during which:
• the proving entity (P) communicates to the verification entity (V) the result of calculation of the distance between the candidate and reference biometric data, and said data,
• the proving entity (P) generates from each datum a function of a number d of variables fa(i1, . . . , id), fb(i1, . . . , id) where d=log2 n, defined for each variable on the set {0,1}, by reformulation of the index i of each component (ai, bi) in binary format,
• the proving entity (P) generates from each function a polynomial of d variables ã(x1, . . . xd), {circumflex over (b)}(x1, . . . xd) defined on d where is a finite field, such that each polynomial ã, {circumflex over (b)} coincides with the corresponding function fa,fb on the set {0,1}d, and generates from the polynomials ã, {circumflex over (b)} a polynomial p(x1, . . . , xd) of d variables of the same expression as that of the distance between the data, and
• the proving entity (P) and the verification entity (V) engage in a Sumcheck protocol applied to the polynomial p to verify the result of the calculation of the distance between the data.

A computer program product, comprising code instructions for execution of a method comprising steps of:

• acquisition of an image and conversion of said image into a biometric datum comprising n components,
• acquisition of a biometric reference datum recorded in an identity document, the datum comprising n components,
• comparison of the two data by calculation of a distance between the two data comprising calculation of a polynomial of the components of the data,
• communication of the result and of said data to a verification entity,
• generation from each component ai, bi of each datum of a function of a number d of variables a(i1, . . . , id), b(i1, . . . , id) where d=log2 n, defined for each variable on the set {0,1}, by reformulation of the index i of the component ai, bi in binary format,
• generation, from each function, of a polynomial of d variables ã(x1, . . . xd) {circumflex over (b)}(x1, . . . xd) defined on a finite field, such that each polynomial ã, {circumflex over (b)} coincides with the corresponding function a,b on the set {0,1}d, and generation, from the polynomials ã and {circumflex over (b)} of a polynomial p(x1, . . . , xd) of d variables of the same expression as that of the distance between the data,
• engagement, with the verification entity, in a Sumcheck verification protocol applied to the polynomial p,
• when said program is executed on a computer.