Classifications

• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
  • H04L9/30—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy
  • H04L9/3093—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy involving Lattices or polynomial equations, e.g. NTRU scheme
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
  • H04L9/32—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials
  • H04L9/3226—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials using a predetermined code, e.g. password, passphrase or PIN
  • H04L9/3231—Biological data, e.g. fingerprint, voice or retina
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
  • H04L9/32—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials
  • H04L9/3236—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials using cryptographic hash functions
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L2209/00—Additional information or applications relating to cryptographic mechanisms or cryptographic arrangements for secret or secure communication H04L9/00
  • H04L2209/34—Encoding or coding, e.g. Huffman coding or error correction

Definitions

• the invention lies in the field of cryptography. It relates more specifically to a method for regenerating a secret using a user's biometric data, the secret having been previously selected by the user or by a system from which the user will authenticate in the to come up.
• the invention finds a particularly interesting application in the authentication and identification of users. It can also be used to regenerate personal data of the user, for example to regenerate a private key of a private key / public key pair.
• a biometric authentication system is a measurement system based on the recognition of characteristics specific to the individual, such as his fingerprint, the shape of his hand, the iris of his eye, his voice, the shape of his face.
• the biometric authentication can be done by comparing a current biometric data item with a reference biometric data item, or by comparing a secret generated from the characteristics of the biometric data item.
• the first authentication family has the disadvantage of having to store the biometric reference data: the centralized storage of such data is very controlled in some countries like France, and storage on a user medium is vulnerable to theft or loss. of support.
• the protection of biometric data is crucial because biometric data is not revocable: one's fingerprint can not be replaced by another. In addition, this is personal data that should not circulate without the consent of their owner.
• the second family overcomes the problem of storing biometric data because the authentication is done by comparing secrets generated from the biometric data, and not by comparison of the biometric data themselves.
• Several authentication methods are known based on the generation of a key from the biometric data.
• Fuzzy Commitment A Fuzzy Commitment Scheme, A.Juels, M.Wattenberg.In 6th ACM Conference on Computer and Communication Security, 1999. http://citeseer.ist.psu.edu/iuels99fuzzv.
• htmn proposes to generate from a reference biometric data item E of the user, a code word c of an error correction code, to publish the difference between the biometric data item and the code word, as well as the image h (c) of c by a hash function, or hash function, h
• the authentication of the user is successful if his current fingerprint E 'is sufficiently close to E that a word of code c 1 closest to ((E) + E ') is equal to C.
• this method only partial information (cE) of the
• this method is not well adapted to a representation of a fingerprint by a set of points, nor is it intended to account of biometric variations too important.
• the patent application published under No. US2002 / 0120592 discloses a method of authenticating a user from data that may vary slightly, such as for example biometric data.
• the method consists in generating a secret for the user, the secret being represented by a polynomial P, and in hiding the value of P so that only the legitimate user is able to recover the value of the secret represented by P.
• the set R2 is intended to scramble the information from the set R1.
• the invention relates to a method of representing a secret from a biometric data of a user, the secret being represented by a polynomial P of degree n, the method being characterized in that it comprises :
• CM error correction code
• F stable and ordered representation
• the representation method according to the invention only provides partial information on the secret and the reference biometric data of the user, more specifically on the tolerated difference between the reference biometric data and a current biometric data in order to be able to assimilate the current biometric data to the reference biometric data. The calculation of this difference is based on the use of the error correction codes.
• the data provided by the representation method according to the invention are published, they do not provide information to obtain the reference biometric data of the user.
• no information is provided on the error correction code since it is the image of this code by a hash function that is published.
• Such a function having as property that for all x whose image H (x) is known by the hash function, then it is very difficult to calculate y such that H (x) H (y).
• the stable and orderly representation of the biometric data of the user is divided into k parts.
• this cutting makes it possible to make the process less sensitive to the biological variations inherent in the biometric data. For example, an impression is sensitive to many factors: ambient temperature, finger position on the sensor, finger cut.
• the representation method comprises a step of calculating the stable and ordered representation (F) of the reference biometric data of the user.
• the k couples of values ((q - fi), H (q)) are published.
• the publication of value pairs does not involve the publication of the biometric data of the user. It is crucial that such data is not published. Indeed, the biometric data is not revocable, its flight represents a huge risk for any secure access to systems or applications based on this biometric data.
• the risk of stealing the biometric data of the user is zero.
• the invention also relates to a method of regenerating a secret from at least one current biometric data of a user, the secret being represented by a polynomial (P) of degree n, the method being characterized in that He understands :
• a correction step during which, for a stable and ordered representation (F ') of the current biometric data of the user divided into k parts (fo 1 ,..., fk-i'), it is sought k codewords (C 0 ', ..., CM') of an error correction code, such as a current comparison between the i- th code word sought (c, 1 ) and the i th part (f, 1 ) of the current representation (F 1 ) is closest to a reference comparison (c, - f,), the comparison of reference (c, - f,) being calculated consecutively to an enrollment step in which k points (p 0 , ..., p ⁇ -i) of the polynomial (P), k> n randomly selected are encoded in k code words (c 0 , ..., c k-1 ) of an error correction code and a stable and ordered representation (F) of a reference biometric data item of the user is divided into k parts (f 0
• the secret that the user must find is the polynomial P, of degree n.
• P the polynomial
• a secret associated in a prior step to a user, is encoded in such a way that it can only be reconstructed using the biometric data of the legitimate user.
• the method according to the invention allows to authenticate / identify a user through his biometric data by using a secret that is revocable and configurable.
• a secret that is revocable and configurable.
• the secret is also configurable since a different secret can be chosen for each application, system or network that implements the method according to the invention.
• the regeneration method comprises a step of calculating the stable and ordered representation (F ') of the current biometric data of the user.
• the degree n of the polynomial is equal to 8. It has been noted that by dividing the representations of the biometric data of the users used in the representation processes of a secret and regeneration of a secret according to the invention in 16 parts, an illegitimate user never found 8 points of the polynomial, while a legitimate user found more than 8 points of the polynomial in 60% of cases. Thus, by choosing to represent the secret by a polynomial of degree 8 and by choosing to split the representations of the biometric data of the users in 16 parts, one overcomes a problem of false positives: one does not identify / not authenticate a user by to a reference representation of a biometric data of another user.
• the invention also relates to the use of the method of regeneration of a secret according to the invention for regenerating a private key of a private key / public key pair.
• a private key / public key pair is associated with an user.
• the user keeps his secret key in his possession, for example on a support that is personal, for example a USB key (the English "Universal Serial Bus"). It accesses its support for each cryptographic operation requiring its secret key, for example during an authentication or during a cryptographic signature.
• a mobile user can regenerate his private key on demand, which avoids having to store it.
• the invention also relates to a device for representing a secret from a biometric data of a user, the secret being represented by a polynomial (P) of degree n, the device being characterized in that it comprises:
• enrollment means arranged to encode k points of the randomly selected polynomial in k code words of an error correction code, and to cut out a stable and ordered representation of a reference biometric data item of the user; k parts (fo, ..., fk-i), and
• calculating means arranged for calculating k pairs of values ((q- fi), H (Ci)), such that the i-th pair comprises a reference comparison (ci-fi) between the i-th codeword (Q) and the i-th part (fi) of the reference representation (F), and an image of the i-th code word (Cj) by a hash function (H).
• the invention also relates to a device for regenerating a secret from at least one current biometric data of a user, the secret being represented by a polynomial (P) of degree n, the device being characterized in that it comprises: correction means arranged to search, for a stable and ordered representation (F ') of the current biometric data of the user divided into k parts (f o ⁇ ..., W), k codewords (C 0 ', ..., Ck-1 1 ) of an error correction code, such as a current comparison between the searched code word i (Q 1 ) and the i-th part ( fi 1 ) of the current representation (F ') is the closest to a reference comparison (Cj - fj), the reference comparison (c, - fi) being calculated consecutively to an enrollment step during which k points (po, ..., PM) of the polynomial (P), k> n randomly chosen are encoded in k code words (Co C M ) of an error correction code and
• the invention also relates to a device for collecting a biometric data of a user, characterized in that it comprises means for calculating a stable and ordered representation (F, F 1 ) of a biometric data item of a user, adapted to be:
• k-parts ((f 0 , ..., fk-i), (fo-, .... fk-r)), where k is the number of points chosen randomly in a polynomial of degree n, k > n, said polynomial representing a secret of a user, the k points of the polynomial being encoded in k code word ((C 0 , ..., c k- i), (C 0 ', ..., c k- i ') an error correction code, and
• the invention also relates to an authentication system comprising:
• a device for regenerating a secret from at least one current biometric data of a user according to the invention.
• the invention also relates to a computer program on a data carrier and loadable in the internal memory of a computer, the program comprising portions of code for performing the steps of the method of representation of a secret from biometric data according to the invention when the program is executed on said computer.
• the invention also relates to a partially or completely removable data storage means comprising computer program code instructions for performing the steps of a representation method according to the invention.
• the invention also relates to a computer program on a data carrier and loadable in the internal memory of a computer, the program comprising portions of code for the execution of the steps of the process of regeneration of a secret from at least one biometric data item according to the invention when the program is executed on said computer.
• the invention also relates to a partially or completely removable data storage means comprising computer program code instructions for executing the steps of a secret regeneration method according to the invention.
• FIG. 1 shows the steps of the method according to FIG. invention
• FIG. 2 is a functional representation of an authentication system according to the invention comprising a device for representing a secret of a user from a reference biometric data item and a device for regenerating a secret. from at least one current biometric data of the user;
• FIG. 3 is a functional representation of a sensor device of a biometric data of the user according to the invention.
• minutiae characteristic points of a fingerprint
• a minutia is a point which is on the change of continuity of papillary lines.
• Authentication of a fingerprint is then done by comparing the position of the minutiae with respect to a reference template (the term commonly used is the English term "template”).
• a second characterization of a fingerprint is done by texture analysis. analysis texture is described in detail in AKJain, S.Prabhakar, L. Hong and S.Pankanti; "FingerCode: A Filterbank for Fingerprint Representation and Matching", in Proc. IEEE Conf.
• Texture analysis makes it possible to characterize a fingerprint by analyzing the image around the morphological center of the impression after application of Gabor filters.
• the imprint is then characterized by a set of 8 vectors of 80 components each, the components being numbers between 0 and 7.
• Each of the vectors corresponds to the transformation of the image after application of a Gabor filter.
• the component is then the average of the differences in the gray average of the image in a paving sector.
• the fingerprint is characterized by a vector of 640 components.
• the vector thus obtained is called "fingercode”.
• the authentication of a fingerprint is then done by comparing the vector representations of the fingerprints.
• a user is authenticated if the distance between the current vector representation and the reference vector representation is less than a fixed threshold.
• the distance used is the Euclidean distance. It is the texture analysis technique that is used in the invention.
• Figure 1 shows the steps of the method of extracting a secret from biometric data.
• the invention aims to associate a secret to a user so that only the legitimate user can find the secret from his biometric data.
• the method comprises two large phases 1, 2.
• a first phase 1 corresponds to the representation of a secret specific to a user from a biometric data of the user. This phase is to be performed for each secret that the user holds, especially in the case where different secrets are used to protect access to different systems or applications.
• the second phase 2 corresponds to the regeneration of the secret from a current biometric data of the user. With the second phase 2, it is verified that the secret of the user is found thanks to his current biometric data.
• the second phase corresponds to a phase of authentication of the user; it is performed at each access control of the user to a system or an application whose access is protected by the method according to the invention.
• Phase 1 of the process according to the invention comprises the steps 10, 11 and
• a secret s is chosen in the form of a sequence of digits.
• the secret is represented in the form of a polynomial P of degree n.
• a step 11 of enrolling the user, following the choice of the polynomial P carried out in step 10, comprises sub-steps 11-a, 11-b and 11-c.
• sub-step 11-a it is randomly chosen k points p 0 , ..., p ⁇ -i on the polynomial P, with k> n.
• the k points of the polynomial P are encoded in k code words C 0 , ... c k - i an error correction code.
• C 0 encode (po)
• ..., en encode (p k- i)
• encode represents the error correction code used.
• the Reed Solomon code is used.
• the vector representation F, or fingercode F consecutive to the encoding by the error correction code of the k points of the polynomial P carried out in the preceding step, the vector representation F, or fingercode F, of a biometric reference data of the user.
• the biometric data used is for example the fingerprint of the user.
• the calculation of the fingercode corresponds to a characterization of the reference fingerprint of the user by the texture analysis technique.
• the representation F thus obtained of the reference biometric data is stable and ordered.
• the stable and orderly representation F of the reference biometric data of the user is divided into k parts f 0 , ..., fk-i.
• the taking of the user's reference print necessary to perform substep 11-c is performed independently of step 10 and sub-steps 11 -a and 11-b, but prior to sub-step 11-c of calculating the fingercode.
• a calculation step 12 following step 11, it is calculated k pairs of values such that the i-th pair, 0 ⁇ i ⁇ k-1, corresponds to ((f, - c,), H ( C)), where H is a hash function.
• the i-th pair comprises as a first value, a comparison between the i-th code word c, and the ith part f, of the reference representation F of the biometric data, and as a second value the image by the hash function of the i-th code word C ,.
• An example of a hash function is "SHA-1" (from the English "Secure Hash Algorithm-1").
• the pairs of values obtained in step 12 are published.
• the pairs of values are made available on a server accessible from a public network such as the Internet or Intranet type network.
• the second phase 2 corresponds to the authentication phase of the user and comprises the steps 14, 15 and 16.
• a step 14 it is proceeded to the capture of a current biometric data of the user.
• the vector representation F ', or fingercode F', of the current biometric data of the user is calculated.
• the representation F 'thus obtained of the current biometric data of the user is stable and ordered.
• the stable and orderly representation F 'of the current biometric data of the user is divided into k parts fo', ..., fk-
• step 15 subsequent to the computation and division of the stable and ordered representation of the user's current biometric data item carried out in step 14, it is searched for k code words c, ', 0 ⁇ i ⁇ k- 1, an error correction code such that the i-th code word c, 'is the closest to (c, - f,) + f,'.
• Step 15 corresponds to a correction step: if f, ', coming from the current biometric data of the user is sufficiently close to f h coming from the reference biometric data of the user, then the code word c / is equal to the code word c ( .
• a hash function has several known properties.
• a hash function is hard to reverse.
• knowing the image of x by H, H (x) it is difficult to find x.
• s ⁇ ⁇ , .., s m from the same pairs of values (( ⁇ - ci), H (Q))
• the set of secret si, S 2 , ..., s m used to regenerate a master secret s according to the steps of the method according to the invention.
• the user chooses m secret sentences (the term commonly used is the English term "passphrase") mi, m 2 , ... m m and, after regenerating the master secret s, it is derived from the secret master s the secret secrets if, S 2 , ..., s m .
• the safety of the method according to the invention is based on the choice of certain parameters.
• the greater the length of the parameters fj, the more it will be difficult to exhaustively find fi 'which, starting from the published values (here, H (Cj)) will make it possible to find q such that H (decode (Ci - fj + fj ')) H (Ci).
• those skilled in the art can easily increase or decrease the safety of the process by varying the lengths of the parameters fi and code words Cj, as well as the correcting power of the correction code.
• FIG. 2 is a functional representation of an authentication system according to the invention.
• the system 20 comprises a device 21 for representing a secret from a reference biometric data, and a device 22 for regenerating the secret from at least one current biometric data of the user.
• the secret of the user is represented by a polynomial P of degree n.
• the devices 20 and 21 are interconnected via a network 23, for example the Internet network or an intranet network.
• the secret representation device 21 comprises enrollment means 210 arranged to encode k points of the randomly selected polynomial, k> n, into k code words of an error correction code, and to cut out a stable representation and ordinate of a biometric reference data of the user in k parts (fo, ..., f k- i).
• the error correction code is the Reed Solomon code.
• the stable and orderly representation of the reference biometric data of the user is obtained for example by a biometric sensor, connected to the device 21.
• the biometric sensor is not shown in FIG. 2.
• a functional representation of the biometric sensor is provided with the figure 3.
• the secret representation device 21 also comprises calculation means 211 designed to calculate k pairs of values, ((Cj-fj), H (Cj)), such that the ith pair comprises a reference comparison (Cj-i). fj) between the i-th code word Ci and the i-th part fi of the reference representation F of the biometric data, and an image of the i-th code word Q by a hash function.
• the device 22 for regenerating the secret from a current biometric data of the user comprises correction means 220 arranged to search, for a stable and ordered representation F 'of at least one current biometric data of the user cut out in k parts fo ', ..., fk-1 1 , k code words Co' CM 'of an error correction code, such as a current comparison between the i-th searched code word Q 1 and the i and the i th part fi 'of the current representation F' is the closest to a reference comparison Cj-fj . .
• the reference comparison Cj-fj is calculated following an enrollment step during which k points po PM of the polynomial P which represents the secret of the user, chosen randomly, k> n, are encoded in k code words Co, ..., CM of an error correction code. During the enrollment step, it is also calculated a stable and ordered representation F of a user reference biometric data item that is divided into k parts fo, ... f k -i.
• the reference comparison Cj-fj is made accessible to the correction means 220.
• the secret regeneration device 22 also comprises authentication means 221 arranged to verify that the image H (Cj) of the code word ci 'of the current representation F' by a hash function H is equal to the image H (ci) of the code word ci of the reference representation F by the hash function H.
• a hash function H is the function SHA-1.
• Figure 3 is a functional representation of a biometric sensor according to the invention.
• the biometric sensor 30 comprises means 301 for calculating a stable and ordered representation of a biometric data of a user.
• the stable and ordered representation is obtained for example by texture analysis of the biometric data.
• the stable and ordered representation of the biometric data of the user is adapted to be divided into k parts, k corresponding to a number of randomly selected points in a polynomial of degree n, k> n, the polynomial representing a specific secret to the the user and the k polynomial points being encoded in k codewords of an error correction code.
• the error correction code chosen is the Reed Solomon code.
• the stable and orderly representation of the biometric data of the user is further adapted to be compared with the code words of the error correction code.
• the biometric sensor 30 further comprises connecting means 302 arranged for connecting the biometric sensor 30 to a device for representing a secret from a biometric data item according to the invention or to a device for regenerating a secret according to the invention.
• the means 302 are for example a connection type "USB" (the English “Universal Serial Bus”).
• the method according to the invention has been applied to a public key cryptographic system of the "RSA" type (named after the inventors Rivest, Shamir and Adleman) so that nomadic users can regenerate the private key of their private key / public key pair.
• RSA assigned in advance, on demand, so as not to have to store the private key on a support.
• k 16
• degree of the polynomial representing the secret of the user n 8.
• P X 8 + 2X 7 + 3X 6 + 4X 5 + 5X 4 + 6X 3 + 7X 2 + 8X + 9
• the points p 0 are encoded into code words of an error correction code.
• the error correction code chosen in this sample application is the Reed Solomon code.
• the code obtained from the point pi is noted q, 0 ⁇ i ⁇ 15.
• the user U repeatedly applies his finger to a biometric sensor to calculate a stable and ordered representation F, or fingercode, of the representative biometric data.
• k 16 pairs of values are calculated:
• the 16 pairs of values thus calculated are made public, for example being made available on a server accessible from a public network such as the intemet. Value pairs can also be stored on a smart card user support.
• a first generation of the public key / private key pair RSA is performed for the user, in accordance with the RSA key pair generation algorithm.
• the public key (n, e) is made available to all, for example on a key server, the rest is erased.
• step 14 of the method it is carried out using a biometric sensor with one or more fingerprint captures of the user, and then calculated a stable and ordered representation F ', or fingercode, of the data. biometric.
• the polynomial P is applied the inverse of the algorithm which made it possible to code the secret s into the polynomial P, and thus the secret is found.

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