A distributed calculation method for a metric representing the difference between two data points.

Abstract

A biometric authentication or identification method comprising the distributed calculation of a metric representing a difference between a data item comprising bits () and a data item, the metric being of the form , the method being implemented by a system comprising devices, the method comprising: - for any from 1 to , calculation of at least one intermediate data item by the device with index dependent on the data item and the data item, and transmission to the device with index at least one result comprising or dependent on each intermediate data item, - determination, by the device with index , of the metric , the determination comprising a summation of each result to obtain a value equal to or a value equal to .

Description

Title of the invention: A biometric authentication or identification method comprising a distributed calculation of a metric representative of a difference between two data points technical field

[0001] This disclosure relates to a biometric authentication or identification method comprising the calculation of a metric representing the difference between two data points, advantageously applicable in the field of biometrics. TECHNOLOGICAL BACKGROUND

[0002] Various metrics are known for determining whether two data points are more or less close. The Hamming distance is one of them.

[0003] These metrics are notably used to compare an input biometric data and a reference biometric data previously enrolled and stored in a database.

[0004] Such databases must be kept confidential, as must any processing based on their content, including the calculation of a metric of the type mentioned above. Moreover, in some countries, the creation of such databases may only be permitted if this confidentiality is guaranteed. SUMMARY

[0005] One purpose of this disclosure is to secure the calculation of a metric representative of a gap between two data in the context of authentication or biometric identification.

[0006] To this end, according to a first aspect, a biometric authentication or identification process is proposed, comprising the following steps: - acquisition by a sensor of a biometric data X comprising n bits ( Ai' ..., referring to an individual, - calculation of a metric / (X, Y) representing the difference between biometric data X and a reference biometric data Y, - comparison between the metric f(X, Y) and a predefined threshold, the metric f(X, Y) being of the form: [00071 f(XY) = fxÀX)+Y^f,(x,, Y)+fy(Y)

[0008] where fx is a function depending only on the data X, / is a function depending only on the data Y, and for all i from 1 to n, f. is a predefined function the process being implemented by a system comprising m + 1 devices ( ..., Dm+l) distinct having respective indices ranging from 1 to m + 1, with w 2, the calculation of the metric comprising: - for any j from 1 to m, calculation of at least one intermediate data point by the device with index j (Pf), each intermediate data point depending on the data point X and the data point Y, and transmission to the device with index m + 1 (Dm+i) of at least one result including or depending on each intermediate data point, - determination, by the m + 1 index device of the metric f (X, Y ), the determination including a summation of each result to obtain a value equal to £^x. y) or a value equal to ^f^x- y)

[0009] The method according to the first aspect may also include the following optional features, taken alone or in combination whenever technically possible.

[0010] In a first embodiment: - the data X forms a vector of K data ..., XK), where for all i from 1 to K, the data X( forms a vector of / bits xK(j ..., xK(ij )+i) ' - the given Y forms a vector (y .... Yp), where for all i from 1 to K, Y is an integer, - we have « = Kl, where K > 1 and / > 1, - for all i from 1 to K and for all P from 1 to / , we have:

[0011] Y)=cpJ(Y)jcK{ii)+P

[0012] where cpj( y ) is a scalar whose value can depend on i, P and the data î, - for all j from 1 to m, the device of index j (Df) calculates / intermediate data Rf j ( X ),... , Rjj( X ), each intermediate data being calculated as follows: for all P from 1 to / , 100131 Rj^X] = ^DPFi / a, c,X r\,xKi

[0014] where a is a predefined constant, - for all i from 1 to K and for all P from 1 to 1, DP F \p ( a, cpi ( Y ) ; • ) ,..., DPFm,p(a> cp,i( Y ); ■ ) are functions satisfying the following conditions: 100151 l 0 six * a

[0016] In this first embodiment, the process may comprise the steps following: - for all j from 1 to m, calculation by the device with index j (Pp) of a result Rj ( X ) from the sum of the intermediate data Rj j ( X ),... , Rj / ( X ), - for all j from 1 to m, transmission of the result Rj(X) to the index device

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[0033] m+1( / ^), - summation, by the device with index m + 1 (Dm+i), of the m results R^X),..., Rm(X) so as to obtain the value of the term y' Preferably, in which, for all j from 1 to m, the result R^X) is obtained by summing the intermediate data Rj^X),... , Rjj(X) and a term / .Y stored by the device of index j and in which: Y" / x In a variant of the first embodiment, allowing us to obtain a metric constituting a scalar product, we have: a = 1 r x (*)= / y (y)=o and for all P from 1 to 1 and for all i from 1 to K: c^Y) = 21^ In another variant of the first embodiment, allowing us to obtain a metric constituting the square of a Euclidean distance, we have: a = 1 / y (x)=E^ and in which, for all P from 1 to l and for all i from 1 to K; ^) = -2¾ In another variant of the first embodiment allowing for obtaining a Mahalanobis distance, we have: a — 1 fx(X) — XT MX where M is a predefined square matrix of the form ( , v ' 7 u,v=lv-J£ and in which, for all P from 1 to / and for all i from 1 to K; cpJ(Y) = -2'Ï^M^Y, In a second embodiment, allowing us to obtain a metric constituting a Hamming distance, we have: - the data Y forms a bit vector v Y vr yn) - we have:

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[0048] - for all i from 1 to n, we have: y.(%. y)=Xi®y. where ® is an exclusive disjunction, - for any j from 1 to m, the device with index j (Df) calculates an intermediate data point X), as follows: U',) in which DPF^0, 1; • ) DPFm{0,t, • ) are m functions satisfying the following conditions: F" DPF (0 kà) = î 1 LJ=}R>FYA^x) |() six5t0 in which DPF[ (1,1; •),•••, DPFm (1,1; • ) arem functions satisfying the following conditions: Lj=PPFj(1^x) = { Q And in which the device with index m + 1 (Dm+l) obtains a value equal to f .(x- F) P31 summation of the m results / y (X),• • ■, Rm(X) • Preferably, the comparison includes calculations distributed over the m + 1 devices (Di,..., It is also proposed, according to a second aspect, a computer-readable memory storing instructions executable by the computer for the execution of the steps of the process according to the first aspect. A third aspect also proposes a biometric authentication or identification system comprising: - a biometric sensor configured to acquire biometric data X comprising n bits (xi' • • • ' relating to an individual, - a calculation system to calculate a metric f{X, y} representing a difference between biometric data X and a reference biometric data Y, - comparison between the metric f(X, Y) and a predefined threshold, in which the metric f(X, y) is of the form: f(X. r) = fx(x) + Y) (Y) where fx is a function depending on the data X, f is a function depending on the data Y, and, for all i from 1 to tl, f is a predefined function, the calculation system comprising m+ 1 distinct devices (Dy ■■■ , Dm+î) having respective indices from 1 to m+ 1, with m > 2, in which: - For any j from 1 to m, the device with index j (^j) is configured to compute at least one intermediate data point, each intermediate data point depending on the data point X and the data point Y, and to transmit to the device with index m + 1 (Dm+\) at least one result comprising or depending on each intermediate data point; - the device with index m + 1 (Dm+}) is configured to determine the metric f(X, K), the determination comprising a summation of each result to obtain the value of the term JXr > ' DESCRIPTION OF FIGURES

[0049] Other features, purposes and advantages will become apparent from the following description, which is purely illustrative and not limiting, and which should be read in conjunction with the accompanying drawings on which:

[0050] Fig. 1 schematically illustrates a biometric authentication or identification system according to one embodiment.

[0051] The [Fig.2] is a flowchart of steps of a biometric authentication or identification process according to one embodiment.

[0052] Throughout the figures, similar elements bear identical references. DETAILED DESCRIPTION OF THE INVENTION

[0053] 1) Biometric authentication or identification system

[0054] With reference to [Fig.1], a biometric authentication or identification system 1 comprises a biometric sensor 2 and a computing system 4.

[0055] The biometric sensor 2 is configured to acquire biometric data X relating to an individual. The biometric data X can be from a fingerprint, an iris scan, or a face, for example. The biometric data X comprises n bits (xi' • • • ' A").

[0056] The calculation system 4 has the function of carrying out processing, in particular the calculation of a metric / (XK) representative of a difference between the biometric data X acquired by the biometric sensor and a biometric data Y, The biometric data Y constitutes a reference data previously enrolled (for example by means of the biometric sensor 2 or another biometric sensor).

[0057] The calculation system 4 comprises m + 1 distinct devices Db ... , Dm+i having respective indices from 1 to w + 1, with m > 2. In particular, it is possible to choose m = 2. The devices Dlt ... , Dm+A are distant from each other, and interconnected by a network of any type, wired or wireless.

[0058] The m devices Db ..., Dm are intended to perform calculations in parallel; these calculations constitute different contributions to the calculation of the metric f(X, Y).

[0059] For any j from 1 to m, the device includes an input interface for receiving the biometric data X, and for also receiving the biometric data Y or pre-calculated data that depends on the biometric data Y.

[0060] In one variant, the biometric data Y is stored in a local or remote database to which the device D has access.

[0061] In another advantageous embodiment, pre-calculated data that depends on the biometric data Y is stored by the device Dj, and the biometric data Y is not stored as such in the computing system 4 or in a local or remote database. Furthermore, each device Dj stores only a portion of the pre-calculated data that depends on the biometric data K. This embodiment is advantageous because it improves the confidentiality of the biometric data K. In certain embodiments that will be detailed later, the pre-calculated data includes functions of the form DP F £p(o, cpj( Y ) ; • ).

[0062] For any j from 1 to m, the device Dj includes at least one processor configured to apply a processing step that contributes to the calculation of the metric / (X, Y). The processor(s) may be of any type, for example, a programmable circuit (ASIC, FPGA) or not. The device Dj further includes a memory that stores a program comprising code instructions to apply this processing step. When the program is executed by the processor(s) of the device Dj,

[0063] For any j from 1 to m, the device Dj includes an output interface for transmitting data to the device Dm+i.

[0064] The device Dm+1 includes an input interface for receiving data from the m devices D^ ... , Dm+b

[0065] The device Dm+i further comprises at least one processor configured to apply processing including, in particular, a final contribution to the calculation of the metric f(X, Y). The processor(s) may be of any type, for example, a programmable circuit (ASIC, FPGA) or not. The device Dm+i further comprises a memory that stores a program comprising code instructions for applying this processing when the program is executed by the processor(s) of the device Dm+i.

[0066] 2) General considerations on the metric f(X, F)

[0067] The calculation system 4 is specifically configured to calculate a metric f(X, Y) of the following form: Y) + f ( Y ) °where fx is a dependent function of the data A, / is a function depending on the data Y, and, for all i from 1 to n, f. is a predefined function.

[0068] The metric f(X, F) can in particular be one of the following metrics: • The dot product of biometric data A and K, • The square of the Euclidean distance between biometric data X and Y, • The square of the Mahalanobis distance between the biometric data X and Y, • The Hamming distance between biometric data X and Y.

[0069] These different embodiments are detailed below.

[0070] 3) Biometric authentication or identification method

[0071] With reference to [Fig.2], a biometric authentication or identification process implemented by system 1 comprises the following steps.

[0072] In an acquisition step 100, the biometric sensor 2 acquires the biometric data X. The biometric data X is transmitted by the biometric sensor 2 to the devices, Dm.

[0073] For any j from 1 to m, the device Dj implements a process designated by reference 102. The process 102y includes the calculation of at least one intermediate data, each intermediate data depending on the data X and the data Y, and the transmission to the device Dm+i of at least one result comprising or depending on each intermediate data.

[0074] In step 104, the device Dm+l determines the metric f(X, Y) using each result produced in the preceding steps. This determination includes, in particular, a summation of each result provided by the devices Dh..., Dm to obtain a value equal to f(xy) or a value equal to f(x-y) + f(y). The summation performed and the value obtained by the device depend on the type of metric being calculated, as will be seen later.

[0075] In step 106, the Dm+i device compares the calculated metric f(X, K) with a threshold. Based on this comparison, the Dm+i device generates an authentication or identification result.

[0076] If the metric f(X, Y) is less than the threshold, then the discrepancy between the biometric data X and Y is considered small. In other words, the biometric data X is considered to correspond to the previously enrolled biometric data Y. In this case, the authentication or identification result generated by system 1 is positive. The individual to whom the biometric data X relates is then authenticated or identified.

[0077] If, on the other hand, the metric f^X, Y ) is not less than the threshold, then the discrepancy between the biometric data X and Y is considered to be high. In other words, the biometric data X is considered not to correspond to the previously enrolled biometric data Y. In this case, the authentication or identification result is negative. The individual to whom biometric data X relates is therefore not authenticated or identified.

[0078] The biometric authentication or identification process can be used in various applications. One of these is to condition access to a secure area, for example a boarding area in a means of transport such as an airplane. 3.1) Dot product

[0079] In a first embodiment, the metric f(X, K) is the dot product of the biometric data X and K.

[0080] The input data for the calculation of the metric f(X, F) are then of the following form: • on an = Kl, where K > 1 and / > 1. • The data X forms a vector of K data points (Xj, ..., XK), where for all i ranging from 1 to X, the data Xf forms a vector of / bits C*k(M)+b • • ■, ' • The data Y forms a vector, YK), where for all i from 1 to X Yi is an integer.

[0081] Furthermore, for all i from 1 to K and for all P from 1 to i, we have: Y)=cpj^ is a scalar whose value can depend on i, P and the data Y.

[0082] More precisely, in the first embodiment, we have for all P from 1 to / and for all i from 1 to K:

[0083] f(X) = f(Y) = 0 Av J

[0084] Furthermore, the processing implemented by the calculation system 4 is then as follows.

[0085]

[0086] The terms cpj(F) can be calculated in a preliminary step, before acquisition step 100, or even, for example, during the enrollment of biometric data Y. Once calculated, these terms cPi(Y) are stored by devices D to Dm. Thus, when biometric data X is subsequently received by the computing system 4, the terms cpi(F) are available. Furthermore, for any j from 1 to m, the device Dj calculates l intermediate data, Rji(X) at step 102y, each intermediate data being calculated as follows. For all P ranging from 1 to / , » (v\ VA nDr? m. v \oùa is a predefined constant equal to 1, and where for all i from 1 to K and for all P from 1 to I, DP F ^P ( a„ cpi (Y ) ; DP F ( a, cpi ( Y ) ; • ) are functions satisfying the The following conditions apply: ^=1DPFpp (a, cp4 (Y); x) = cpj (F) if x = a ^DPFj^a, cp4 (Y); x) = 0 six* a

[0087] Thus, the m functions DPFtp ( «, cpj ( F ) ; DPFm,P ( a, cpi ( F ) ; • ) represent a distribution of a point function (“distributed point function” in English) respectively on the m devices D\ to Dm.

[0088] As previously stated, these m functions (depending on the terms cpi( Y) and a) are preferably calculated in advance and stored in the respective memories of the m devices at Dm, and the biometric data Y is not stored as such in the computing system 4 nor in a local or remote database.

[0089] Then, for any j from 1 to m, the device calculates, in step 102, a result R(X) from the sum of the intermediate data Rj(X), ..., Rjj(X). More precisely, in the first embodiment, the result R(X) is the sum of these data, that is to say:

[0090] R(X} R (X )^nsu^e' For all J going from 1 to m, the device Dj transmits the result R, (X) to the device of index Dm+i.

[0091] Thus, in the first embodiment, the device Dm+i receives m results A) ( X ), • • ■, Rm ( X ) respectively provided by the devices Dx, ..., Dfn.

[0092] To obtain the value f(xy) (and consequently the dot product f(X, F) since f(X) = / .(F) — 0)- the device Dm+l calculates the sum of these X 1 m results, as follows:

[0093] ^,(X)=OA 3.2) Square of the Euclidean distance

[0094] In a second embodiment, the metric f(X.Y) is the square of the Euclidean distance between the biometric data X and Y.

[0095] The input data have the same form as in the first embodiment, and we again have, for all i from 1 to K and for all P from 1 to l: Y) = Y )-XK^hp°Ù YeSt A SCakire d°nt value can depend on i, P and the given Y.

[0096] However, unlike the first embodiment, we have for all P ranging from 1 to / and for all i from 1 to K; ^) = -2¾

[0097] Furthermore, we have:

[0098]

[0099] Therefore, in the second embodiment, it is necessary to calculate the terms f(X) and f{Y), which are not in principle nuisance unlike in the first embodiment. The term f(X) can be calculated by one of the m + 1 devices of the computing system 4 from the biometric data X, for example by device Dm+1 or one of of the other devices in the system.

[0100] In an advantageous embodiment, the term f(X) is calculated by an associated device to biometric sensor 2 (and not necessarily part of the calculation system 4) then is transmitted to device £>„)+1 or to one of the other devices in the system which can then include it in its result which will then be transmitted to device Dm+i.

[0101] In a simple variant, the term f { Y) is stored in advance by the device D^. The term f (Y) can then be calculated in advance, before the acquisition step 100, by any one of the devices of the computing system 4. In this simple variant, the m results Rf( X) are calculated as in the first embodiment, and it only remains for the device Dm+i to sum the m results R^X) with the terms f ⇓X) and f { Y) to obtain the metric / (X, Y) constituting the square of the Euclidean distance between the biometric data X and Y.

[0102] In another, more secure and therefore advantageous variant, the calculation of f(Y) is distributed over the m devices at Dm. From the biometric data Y, m terms f(Y, ..., f(Y)) are calculated in advance, these terms satisfying the following condition: 101031

[0104] For any j from 1 to m, the device Dj stores in its memory the term / Y.

[0105] In this other variant, for all j from 1 to m, the device Dj calculates the The result Rj(X) is as follows: 101061

[0107] Thus, each result R^(X) already includes a "portion" of the term f(Y), so that, subsequently, the device Dm+1 obtains a value equal to AWtfir) by summing the m results provided by the devices DY to Dm, respectively. In other words:

[0108]

[0109] Llïl / \ ZZ \ Y) +fr(Y) This alternative variant is more secure, and therefore advantageous, because it allows the metric f(X, Y) to be calculated without explicitly calculating the term f(Y). The value of the term f(Y) therefore cannot be found in the memory of any of the... computing system devices 4. 3.3) Square of the Mahalanobis distance

[0110] In a third embodiment, the metric f(X, K) is the square of the Mahalanobis distance between the biometric data X and Y.

[0111] The input data have the same form as in the first embodiment and in the second embodiment, and we still have, for all i from 1 to K and for all P from 1 to / ; is a scalar whose The value depends on i, P and the data Y, just as in the second embodiment.

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[0118] However, unlike the second embodiment, we have: f (X) = X1MX f ( L) = YtMY°u M is a predefined square matrix of the form ( . Furthermore, we have, for all P going from 1 to l and for all i going from 1 to K; We can therefore see that the coefficients cpj( Y) are also a function of the predefined matrix M. Apart from these differences, the steps implemented in the second embodiment are also repeated in the third embodiment. It should be noted in particular that the two variants handling the term f(Y) differently are applicable to the third embodiment. 3.4) Hamming distance In a fourth embodiment, the metric f(X, K) is the Hamming distance between the biometric data X and Y. In the fourth embodiment, the data Y is simply treated as a bit vector y j.

[0119] Furthermore, we have: f (X) = f (K) =0^.(.¾ Y )= y where © is an exclusive disjunction.

[0120] In the fourth embodiment, for any j from 1 to m, the device Dj calculates an intermediate data Rj(X) as follows in step 102: Rj$ = ^PF^-y,. l;A..) in which DPF,(0,1; ■ ) ..... DPF„„(0.1; ■ ) are functions satisfying the following conditions: ^=lDPFj ( 0,1; x ) = 1 if x = O^pPFj ( 0,1; x ) = 0 if x * 0 and in the club DPF](1,1; ■ ), ..., DPFm{ 1,1; • ) are functions satisfying the following conditions: The functions DPFj(1,1; x) = 1 if x = 1E™ and DPFj(1,1; x) = 0 if x * 1. The m functions DPF^0,!; • ),..., DPFm(0A; • ) represent a distribution of a point function respectively on the m devices D\ to Dm. The m functions DPF^1,1; • ), ..DPFm(1,1; • ) represent a distribution of another point function respectively on the m devices Dv to Dm.

[0121] Thus, in this fourth embodiment, for all j from 1 to m, the device Dj calculates only one intermediate data, constituting a single result Rj(X).

[0122] The device ^„;+i obtains a value equal to f {x- y) P31 summation of the m results R^X),..., R^X). 4) Other implementation variants

[0123] In the preceding text, embodiments have been described in which the comparison between the metric f(X, F) and the threshold is a step 106 implemented by the device D^. Alternatively, it is possible to perform this comparison in a distributed manner, that is, to entrust the devices at Dm with additional calculations producing contributions to this comparison. Such a distribution is known to those skilled in the art and has been described in the paper "Function Secret Sharing: Improvements and Extensions" by Elette Boyle et al., CCS 2016. These contributions can be added to the intermediate data discussed previously, so as to be included in the results that are then transmitted to the device ^m+i.

[0124] Furthermore, embodiments have been described in which intermediate data are summed by the devices at Dm so as to produce results which are then transmitted to the device Dm+i- Alternatively, it is conceivable that the devices Dr at Dm transmit the intermediate data separately to the device Dm+l and entrust the device Dm+X with the task of summarizing them.

Claims

Claims

1. A method of biometric authentication or identification comprising steps of: - acquisition by a sensor of biometric data X comprising n bits (xi' • • ■ ' x«) relating to an individual, - calculation of a metric f(X, Y) representative of a difference between the biometric data X and a reference biometric data Y, - comparison between the metric f(X, Y) and a predefined threshold, in which the metric / (X, K) is of the form: f(X, Y) = fx(X) Y) +fr(Yrùfx is mie function depending only on the data X, f is a function depending only on the data Y, and for all i ranging from 1 to n, f is a predefined function, the method being implemented by a system comprising m + 1 distinct devices (^i, • - • , Dm+\) having respective indices ranging from 1 to JH + 1, with m > 2, and in which the calculation of the metric comprises: - for all j ranging from 1 to m, calculation of at least one intermediate data by the device of index j (Df), each intermediate data depending on the data X and the data X, and transmission to the device of index m+ 1 (Dm+]) of at least one result comprising or depending on each intermediate data, - determination, by the device of index m + 1 of the metric f (X, Y), the determination comprising a summation of each result to obtain a value equal to f (x- Y) or a value

2. The method of claim 1, wherein: - the data X forms a vector of K data (Xj, ..., XK), where for all i going from 1 to X, the data X, forms a vector of / bits (XK(fl)+b • • •, xK(i-ï)+l), - the data Y forms a vector (Xj, ..., Y where for all i going from 1 to X, Yi is an integer, - on an = Kl, where X > 1 and / > 1, - for all i ranging from 1 to X and for all P ranging from 1 to / , we have: / ^-(,.,)+,,(^(+1)+^ scalar whose value can depend on i, P and the data X, - for all j ranging from 1 to m, the device with index j (Dj) calculates / intermediate data Rj [(X),... , Rji( X), each intermediate data being calculated as follows: for all P ranging from 1 to / , j? (y\ _ / w 6, \where a is a predefined constant ~ j^a, Cp^ ï ),xK(iAyp), - for all i ranging from 1 to K and for all P ranging from 1 to 1, DP F ( a, cPj ( Y ) ; DPFm>P ( a, cpj ( Y ) ; ■ ) arem functions satisfying the following conditions: Y^pPFj^ a, cp^( Y); x) = cpj( Y) if x = « E ^DPFj,p [ a, cPj ( Y ) ; x ) = 0 if x * a.

3. Method according to claim 2, comprising the following steps: - for any j ranging from 1 to m, calculation by the device of index j (Dj) of a result Rj(X) from the sum of the Z intermediate data R^X),...,Rjj(X), - for any j ranging from 1 to m, transmission of the result R^X) to the device of index m + 1 (Dm+l\ - summation, by the device of index m+ 1 (Dm+}\ of the m results / ? f ( X ), • • ■, Rm ( X ) so as to obtain the value of the term y)'

4. Method according to any one of claims 2 and 3, in which for any j ranging from 1 to m, the result R^X^ is obtained by summing the l intermediate data Rjj ( X ),... , Rjj ( X ) and a term f .Y stored by the device of index j (Dj^ and in which: YXjY = fy(Y).

5. Method according to any one of claims 2 to 4, in which: a = ly (X) = f (Y) = O and for all P ranging from 1 to 1 and for all i ranging from 1 to K: cpi(Y)=2'^.Y,

6. Method according to any one of claims 2 to 4, in which: a=1fx(X) = £^XlfY(Y) =E*y2and in which, for all P ranging from 1 to / and for all i ranging from 1 to K; epJ(Y) = -2p.Yt

7. Method according to any one of claims 2 to 4, in which: a = ïf (X ) = XT MX f (Y} = YtM F°ù is a predefined square matrix of the form ( M, and in which, for all P ranging from 1 to l and for all i ranging from 1 to K; ^.,(7) = -2^^7,.

8. Method according to claim 1, in which: - the data Y forms a bit vector / yy Y - we have: f ( X ) = / ( K ) =0- for all i ranging from 1 to n, we have: f .(x^ y) = Xj-^ypù ® is an exclusive disjunction, - for all j ranging from 1 to m, the device of index j (Dj) calculates an intermediate data Rj(X), as follows: R^ = ^flPF^-y^ l;j,)in which DPF](0,1; DPFm(Q^ • ) are m functions satisfying the following conditions: Lj=1 DPFj( 0, hx ) = 1 if x = 6 Lj=pPFj ( 0,1; x ) = 0 if x * 0 in which DPFf(l ,1; • ), ■ ■■, DPFm( 1,1; • ) are m functions verifying the following conditions: T"1 W?, yi / 77 4. LJ=iDPFj(1,1; x ) = 1 if x = iL^DPFj( 1,1; x ) = 0 if x * let in which the device of index 1 (Dm+l) obtains a value equal to f (x- Y ) P31 summation of the m results R} (X ), • • •, Rm ( X ) •

9. Method according to the preceding claim, in which the comparison comprises calculations distributed on the 1 devices (Dj,..., Dm+ù-

10. A computer-readable memory storing computer-executable instructions for performing the steps of the method of any one of claims 1 to 9.

11. Biometric authentication or identification system comprising: - a biometric sensor configured to acquire a biometric data item X comprising n bits (xi' • • • ' x«) relating to an individual, - a calculation system (4) for calculating a metric f(X, y) representative of a difference between the biometric data item X and a reference biometric data item Y, - comparison between the metric f(X, Y) and a predefined threshold, in which the metric f(X, Y) is of the form: f(X, Y) =fx(X) + £“ / ,.(*„ Y) + function depending on the data X, f is a function depending on the data Y, and, for all i ranging from 1 to n, / . is a predefined function, in which the calculation system (4) comprises m + 1 distinct devices ( Db .... Dm+1) having respective indices ranging from 1 to m + 1 , with m > 2, in which: - for any j ranging from 1 to m, the device of index j (Df) is configured to calculate at least one intermediate data item, each intermediate data item depending on the data item X and the data item Y, and to transmit to the device of index 1 (Aw+i) at least one result comprising or depending on each intermediate data item, - the device of index m + 1 is configured to determine the metric / (X, Y), the determination including a summation of each result to obtain the value of the term y " f / ry ) ■

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