METHOD OF CONFIDENTIAL INTERROGATION OF A GEODEPENDANT SERVICE BY HOMOMORPHIC CRYPTOGRAPHY

专利摘要:
The invention relates to a method for confidential interrogation (PIR) by a user of a server equipped with a database. The user constructs (220) from the index of the desired record a vector (Vi) encrypted by a homomorphic probabilistic cryptosystem and transmits (230) to the server a query having as argument this vector. The server performs (240) a scalar product between the vector (O) of the records of the database and returns (250) the result to the user. The user decrypts (260) the dot product to obtain the desired record. The present invention applies in particular to the interrogation of a geo-dependent service (LBS) and more particularly to navigation by masked routes.
公开号:FR3040842A1
申请号:FR1558159
申请日:2015-09-03
公开日:2017-03-10
发明作者:Renaud Sirdey；Oana Stan
申请人:Commissariat a lEnergie Atomique CEA；Commissariat a lEnergie Atomique et aux Energies Alternatives CEA；
IPC主号:

专利说明:

CONFIDENTIAL INTERROGATION METHOD OF A GEODEPENDENT SERVICE BY
HOMOMORPHIC CRYPTOGRAPHY
DESCRIPTION
TECHNICAL AREA
The present invention particularly relates to the field of location-based services or LBS (Location Based Services) services. An important application of the invention relates to the field of masked route navigation.
STATE OF THE PRIOR ART
Location-based services (LBS) have grown dramatically in recent years with the advent of third- and fourth-generation smart mobile devices. LBS services include point of interest (POI) search, location of a user, and route search.
LBS services have the common point of providing information depending on the position of the user. The position of a user being sensitive information, the services in question must be able to guarantee confidentiality and respect for the privacy (privacy) of the user. This requirement is all the more necessary as the LBS service can be delivered off-site using a cloud computing platform.
Various schemes have been proposed to ensure the confidentiality of user location data: Trusted Third Party (TTP), semi-distributed schema using at least two independent entities, client-server architecture, collaborative schema confidentiality distributed within an ad hoc network. The client-server architecture has the advantage of not relying on a trusted third party. However, the preservation of confidentiality requires that the server, considered a priori unreliable, can provide the information requested by the user without the position of the latter being revealed to him. Such a confidential interrogation method, in other words without any possibility for the service provider to have access to the plain-text argument of the user's request, in this case his position, is called the PIR method (Private Information Retrieval).
Fig. 1 illustrates the principle of a PIR method in a client-server architecture.
The server of an LBS service provider, 110, has a database, 130 which contains N records, either
each record being constituted by an information element.
A user (or client) 120 sends a request Q (i) where i is an index parameterizing the position of the user, who wishes to actually obtain the information element Ot from the database. The request Q (i) is encrypted so that it is impossible for the server to find the index value i. The server 110 calculates from the table O and the request Q (i) a result R (0, Q (i)) by means of a mathematical transformation and this result is returned to the user. This decrypts the result R (0, Q (i)) to obtain the element Ot.
An example of a PIR method can be found in the article by G. Ghinita et al. "Private queries in Location Based Services: anonymizers are not necessary" published in Proc, of Sigmod 2008, pp. 121-132. This PIR method ensures the confidentiality of the user's position thanks to the intractability of the quadratic residue problem which makes it extremely difficult to determine if an integer is a quadratic residue modulo n, where n-q1q2 is an integer with q1 , q2 large prime numbers, without knowing qx and q2. The PIR method described in this article uses a table in which each cell corresponds to a position and contains the list of POIs closest to that position. It allows a user to get the POIs closest to him.
Although this PIR method provides a high degree of confidentiality, it is relatively complex and requires a large number of calculations.
The object of the present invention is therefore to propose a method of confidential interrogation of a service provider, in particular a geo-dependent service provider, which is simpler than that of the prior art while guaranteeing a degree high confidentiality. A subsidiary object of the present invention is to be able to offer a user a navigation service with hidden routes.
STATEMENT OF THE INVENTION
The present invention is defined by a method of confidential interrogation of a server by a user, said server being equipped with a database represented by a vector of records, in which: the user constructs a vector V. whose all elements except that of an index i are zero ciphers and whose index element i is a cipher of one, the cipher being performed by means of a probabilistic cryptosystem verifying the following homomorphic properties:
where (sk, pk) is a private and public key pair of the user, Encpk is an encryption operation by means of the public key, Decsk a decryption operation using the private key, a, b are clear, Θ is an operator on the cipher space and ® is an operator between the clear space and the cipher space; the user transmits to the server a request having argue for the vector V; the server performs a scalar product between the vector of the records O and the vector V. and returns (250, 350) the dot product C (thus obtained to the user, the user decrypts the dot product C (to obtain the index registration i of the database.
The cryptosystem can be chosen for example from the Pallier cryptosystem, the Regev cryptosystem and the Fau-Vercauteren cryptosystem.
According to an advantageous embodiment, the records consist of the values taken by a function F known to the server on a set of possible positions of the user.
in a given geographical area. The invention also relates to a method of confidential navigation within a given geographical area, implementing the confidential interrogation method defined above and in which: said geographical area contains a plurality of reference points, each pair reference points being associated with an index; said database contains for each index corresponding to a pair of reference points, a record of an optimal path in the sense of a predetermined criterion between these points, the optimal path being defined by a list of points of reference points; reference (& ρ ...., & β) through which this path passes; the user determines the respective indices (iA, iB) of a pair of starting points, A, and of destination, B, and deduces therefrom the corresponding index i of the pair of points (A, B) ·, - the index record i obtained by decryption of the dot product, C (, provides the user with the route between points A and B.
In a dynamic use, the server periodically or on request updates the optimal paths between the reference points of the geographical area.
Advantageously, the server stores a plurality of vectors V relative to a plurality M of couples of favorite points of departure and destination.
In this case, the user transmits to the server a sub-query specifying among the plurality of preferred point pairs, the couple for which he wishes to obtain a route and that the server returns the dot product between the vector of the recordings O and the vector V. corresponding to this sub-query.
Alternatively, the server periodically performs a scalar product computation between the vectors V relative to the pairs of favorite points and the vector of the records O, the server building a vector C of the scalar products thus obtained.
In this case, the user constructs a second vector LL of size M whose elements except that of an index j are zero ciphers and whose index element j is an encryption of one, the ciphering being performed by means of said cryptosystem, the user transmits to the server a sub-query having for argument the second vector LL.
The server advantageously performs a second scalar product between the vector C and the vector LL and sends the user the second scalar product thus obtained. The user then decrypts the second dot product to obtain the dot product Cit and decrypts the first dot product to obtain the route for the desired pair of points.
BRIEF DESCRIPTION OF THE DRAWINGS Other characteristics and advantages of the invention will appear on reading a preferred embodiment of the invention with reference to the appended figures among which:
Fig. 1 represents the principle of a PIR method known from the state of the art;
Fig. 2 represents a flow chart of the PIR method according to one embodiment of the invention;
Fig. 3 is a flowchart of a masked route navigation using the PIR method of FIG. 2.
DETAILED PRESENTATION OF PARTICULAR EMBODIMENTS
The confidential interrogation method according to the present invention will be described hereinafter in the context of a client-server architecture as previously described in relation to FIG. 1. In a particular embodiment of the invention the server will provide a location-based service (LBS), including the search for points of interest (POI) or a navigation service with hidden routes as described in detail below. However, in its most general form, the invention may find application in other types of services, for example a medical file consultation service.
Whatever the type of service envisaged, the server is equipped with a database containing a plurality of records indexed by an index i. So the database can be considered as a vector
, each element of the vector corresponding to a recording. Without loss of generality, it will be assumed in the following that the recordings are represented by elements of
where n = pq is an integer, product of two (large) prime numbers p and q. The idea underlying the invention is to use a probabilistic cryptosystem having particular homomorphic properties for extracting a record using a simple scalar product.
We first recall that a probabilistic encryption Enc {., R) is an encryption dependent on a random parameter r. The encryption of a clear message m can thus give different enciphered messages Enc (m, r) according to the value taken by the parameter r. However, whatever the value taken by this parameter, the deciphering of Enc {m, r) always restores the clear message m. In other words, there is a decryption function Dec such that:
(1)
It is then recalled that a homomorphic encryption is an Encpk (public key pk) asymmetric encryption verifying the following property:
(2) where X is the space of the clear messages (more simply clear space) and Y is the space of the encrypted messages (more simply called space of the ciphered), + an additive operation in the space of the clears giving to X a group structure, Θ an operation in the cipher space giving Y a group structure. It is thus understood that the Encpk application of (X, +) in (Y, ®) is a homomorphism of groups. If Decsk is the decryption function corresponding to Encpk (where sk is the secret key of the user), property (1) can be expressed alternately by:
(3)
In other words, it is possible to perform an additive operation between two clears from a corresponding operation between their ciphers.
We will assume in the following that
It follows from the foregoing that a homomorphic probabilistic encryption method
check the following relation:
(4) where it has been agreed as before that r is a random parameter, pk is the public encryption key and sk is the secret decryption key. Messages a and b are messages in the clear.
In addition to the additive homomorphism property expressed in (4), it is assumed that the encryption method satisfies the following property:
(5) where ® is an external operation of XxF - »Y and where. is a multiplicative operation in Y. In other words, it is possible to perform a multiplicative operation between two clears from the cipher of one of them. It should be noted that relation (5) is not strictly speaking a property of homomorphism since the starting set is the Cartesian product 1x7. It is therefore not necessary for the cryptosystem to be of FHE (Fully Homomophic Encryption) type.
Probabilistic cryptosystems satisfying conditions (4) and (5), notably the Pallier cryptosystem, in which the encryption of a message 0 <m <n is obtained by:
(6) where r is a random integer such that
is the public key, p, q being two prime numbers of large size. Conversely, the decryption of a cipher is obtained by:
(7) with
mod
is the private key.
Given definition (6), the Pallier cryptosystem checks the following properties:
(8) and
(9)
By comparing the relations (4) - (5) with the relations (8) - (9), we understand that the operations ® and 8 respectively correspond to a multiplication and an exponentiation (modulo n2) in the space of the ciphers Zn2. Other cryptosystems also verify the properties (3) and (4), notably the cryptosystems of Fau-Vercauteren and Regev.
Whatever the cryptosystem chosen, the user wishing to obtain the record 0 (i) of the database builds the following vector:
(10) where rx, ..., rN are draw results of the random variable r. The elements of the vector V are therefore all ciphers of 0 except an element in position i which is an encipher of 1.
The vector V. is transmitted in the form of a request to the server of the service provider. This one is incapable of discerning in vector V the element which corresponds to the cipher of 1.
The server then performs the dot product:
(11) where
and return the result C (which is an encrypted) to the user.
This performs the decryption:
(12) or, successively using the homomorphic properties (4) and (5) of the cryptosystem:
(13)
It is thus understood that the user can thus find the record in clear, Oit of the database without at any time the server is able to know what record it is.
Fig. 2 schematically represents a flow chart of the confidential interrogation method (PIR) according to one embodiment of the invention. In step 210, the user determines the index i of the record he wishes to obtain in the database of the server. In step 220, the user numbers N -1 times the null value
ΙίΦϊ and once the value 1, Enc (Ο, η). He builds the V vector defined by (10). In step 230, the user transmits to the server of the service provider his request having for argument the vector V. In step 240, the server performs, according to the expression (11), the dot product C (of vector O having for elements the records of the database with the vector V. received from the user In step 250, the server returns the encrypted result C (to the user. user decrypts the encrypted result C (to obtain the clear record Ot.
The confidential polling method of the present invention allows a user to have a server evaluate a function F (a) where a is a secret data of the user and where F is a known function of the server. Indeed, the server can compute, or have a third party compute, the list of values
taken by the F function on the set
possible discrete values of a. Set A is ordered and the order relation is known to both the user and the server. The records in the database consist of the F (a,) values
When the user wishes to obtain the value taken by the function F at at, it is sufficient for him to transmit to the server a request having for argument the vector Vj, according to the method of FIG. 2. The server then returns the scalar product C (which is decrypted by the user to find the value F (a (.).
In particular, the values at can be possible positions of a user and the function F can be that of a location-based service. For example, F (a (.) Can give the list of points of interest (POI) closest to the position point at.
The present invention is advantageously applied to a confidential navigation method in the sense that the routes are masked to the server. More specifically, such navigation allows a user to obtain an optimal route, in the sense of a certain criterion, between a starting point and an arrival point without revealing to the navigation server either the starting point or the point of departure. point of arrival, or the route in question. In other words, all the navigation data (starting point, list of points of passage defining the route, arrival point) remain perfectly confidential.
To do this, the navigation server computes or has computed by a third entity, all the optimal paths, in the sense of a certain criterion, between each pair of reference points of the geographical area of interest. The criterion may be for example a minimum distance or a minimum travel time (depending in particular on traffic conditions). The calculation uses a representation of the road network of the geographical area in the form of a valued graph whose vertices are the reference points in question and whose edges have for weight distances or travel times. The search for the optimal path between a starting point and an end point then returns to that of a path of lower weight in the graph in question. This problem is well known in graph theory and several algorithms can solve it effectively, including the Dijkstra or Floyd-Warshall algorithm. The Floyd-Warshall algorithm is preferably used to compute at one time all the shortest paths for all the vertex pairs of the graph.
If we assume that the graph has P vertices, the previous search gives N = P (P-1) paths for all the pairs of points of the graph (it is assumed in general that the graph is oriented and that the weights of the edges opposing meanings between two points may differ). The points of the geographical area are indexed and the pairs of vertices of the graph are ordered according to a total order relation, for example a lexicographic order. The pairs are stored in the database in the form of an ordered list according to this order relation, a record relating to each pair of points in the list containing, in coded form, the list of points defining the optimal path between the first and second points of this couple. Where appropriate, the record will also contain the weight of the optimal path (minimum distance or minimum travel time). Thus, if the points of the geographical area are indexed, a record relating to a pair (iA, iB) may consist of a list of indices kv ...., kQ points defining the path between the starting point A, of index iA, and the destination point B of index iB. The indices k.sub.k, k.sub.Q may be separated using a predetermined separator character and the list of indices may advantageously be encoded by means of a source encoding, so as to reduce the length of the recordings.
It should be noted that the database is generally dynamic, especially when the navigation is performed according to a criterion of minimum travel time. In this case, a network of sensors deployed along the road network makes it possible to determine the state of the traffic and to update the travel times relative to the different edges of the graph. The server or the third-party entity regularly or on request calculates the optimal paths in the graph and updates the database accordingly.
Fig. 3 schematically represents a flow chart of a masked route navigation method using the confidential query method of FIG. 2. In step 310 the user determines the pair of indices (iA, iB) respectively indexing the starting point A and the destination point B of the desired route, and deducing from it the index i of the record containing the optimal path between these two points. In step 320, the user digit TV - 1 null values with
is
and a value 1, either
are random numbers. The user then forms a size vector
the order of the elements being a total order relation of the pairs (jU, v), for example the lexicographic order, the index i being the index associated with the pair (iA, iB) according to this order. In step 330, the user transmits to the server a request having as argument the vector V .. At step 340, the server calculates the dot product
between the vector O whose elements are the records of the database (here the optimal paths) and the vector V received from the user. In step 350, the server returns the encrypted result C. to the user. In step 360, the user decrypts C,, and obtains the list of indices L, ...., kn M '1B 1 of the points of the geographical zone defining the optimal route between points A and B.
It is thus understood that at no time is the server aware of the points A and B (i.e., indices iA, iB) and consequently of the user's route between these points. The user's route is therefore hidden from the server.
When the number P of reference points of the geographical area is high (in other words when the number of vertices of the navigation graph is high), the vector O is very large. In order to reduce the size of the latter, the user can indicate to the server a subregion in which the points A and B are located.
In addition, the user can register with the server a list of requests corresponding to his pair of favorite points of departure and destination. These queries result in a list of favorite V vectors. The server can then periodically calculate the scalar product C (for the preferred V vectors of the list in question.
The scalar products C (can themselves be considered as elements of a vector C of size M substantially smaller than that of the vector O. It is then sufficient for the user to send a subquery, encrypted on the same principle than previously, and making it possible to specify among the favorite requests the one of which it wishes to obtain the route.
Specifically, the user builds a vector
where M is the plurality of starting point and destination point pairs. The server then calculates a second scalar product between the vector C and the vector LL and returns the result to the user. The user decrypts the second scalar product
to obtain the first scalar product C (, then decrypts the first scalar product to obtain the Gold record The second scalar product makes it possible to carry out a confidential extraction of the optimal paths for all the pairs of favorite points of departure and destination, and the first scalar product then makes it possible to extract among the optimal paths thus extracted, the relative route to the desired pair of points among the couples of favorite points.
It is understandable that the server has no knowledge of the pair of favorite points of departure and destination, let alone any knowledge of the one for which it wishes to obtain the optimal route.
The navigation method thus makes it possible to combine a great simplicity of use with a very high level of confidentiality.

权利要求:
Claims (11)
[1" id="c-fr-0001]
1. Method of confidential interrogation of a server by a user, said server being equipped with a database represented by a vector of records, characterized in that: the user constructs (220, 320) a vector V. whose all elements except that of an index i are zero ciphers and whose index element i is a cipher of one, the cipher being performed by means of a probabilistic cryptosystem verifying the following homomorphic properties:

where (sk, pk) is a private and public key pair of the user, Encpk is an encryption operation by means of the public key, Decsk a decryption operation using the private key, a, b are clear, Θ is an operator on the cipher space and ® is an operator between the clear space and the cipher space; the user transmits (230, 330) to the server a request having for argument the vector V; the server performs (240, 340) a scalar product between the vector of the recordings O and the vector V. and returns (250, 350) the dot product C (thus obtained to the user, the user decrypts (260, 360) the dot product C (to obtain the index record i of the database.
[2" id="c-fr-0002]
2. Confidential interrogation method according to claim 1, characterized in that the cryptosystem is a cryptosystem chosen from the Pallier cryptosystem, the Regev cryptosystem and the Fau-Vercauteren cryptosystem.
[3" id="c-fr-0003]
3. confidential polling method according to claim 1 or 2, characterized in that the records are constituted by the values taken by a function F known to the server on a set of possible positions of the user

in a given geographical area.
[4" id="c-fr-0004]
4. Method of confidential navigation within a given geographical area, implementing the confidential interrogation method according to claim 1 or 2, characterized in that: said geographical area contains a plurality of reference points, each pair reference points being associated with an index; said database contains for each index corresponding to a pair of reference points, a record of an optimal path in the sense of a predetermined criterion between these points, the optimal path being defined by a list of points of reference points; reference (kv ...., kQ) through which this path passes; the user determines (310) the respective indices (iA, iB) of a pair of starting points, A, and of destination, B, and deduces therefrom the corresponding index i of the pair of points (A, B) ; the registration of index i obtained by decryption of the dot product, C (, provides the user with the route between the points A and B.
[5" id="c-fr-0005]
5. Confidential navigation method according to claim 4, characterized in that the server updates periodically or on request the optimal paths between the reference points of the geographical area.
[6" id="c-fr-0006]
6. Confidential navigation method according to claim 4 or 5, characterized in that the server stores a plurality of V vectors relating to a plurality M of couples of favorite points of departure and destination.
[7" id="c-fr-0007]
7. Confidential navigation method according to claim 6, characterized in that the user transmits to the server a sub-query specifying among the plurality of couples of favorite points, the couple for which he wishes to obtain a route and that the server returns the scalar product between the vector of the records O and the vector V corresponding to this subquery.
[8" id="c-fr-0008]
8. The method of confidential browsing according to claim 6, characterized in that the server periodically performs a scalar product calculation between the vectors V relative to the couples of favorite points and the vector of the records O, the server building a vector C of the products. scalars thus obtained.
[9" id="c-fr-0009]
9. Confidential navigation method according to claim 8, characterized in that the user constructs a second vector Uj of size M, all elements except that of an index j are zero ciphers and whose index element j is an encryption of one, the encryption being performed by means of said cryptosystem, the user transmits to the server a sub-query having for argument the second vector Lh.
[10" id="c-fr-0010]
10. Confidential navigation method according to claim 9, characterized in that the server performs a second scalar product between the vector C and the vector Uj and returns to the user the second scalar product thus obtained.
[11" id="c-fr-0011]
11. The method of confidential navigation according to claim 10, characterized in that the user decrypts the second dot product to obtain the dot product Cit and decrypts the first dot product to obtain the route for the desired pair of points.

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优先权:

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申请号 | 申请日 | 专利标题

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FR1558159|2015-09-03|

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FR1558159A|FR3040842B1|2015-09-03|2015-09-03|METHOD OF CONFIDENTIAL INTERROGATION OF A GEODEPENDANT SERVICE BY HOMOMORPHIC CRYPTOGRAPHY|FR1558159A| FR3040842B1|2015-09-03|2015-09-03|METHOD OF CONFIDENTIAL INTERROGATION OF A GEODEPENDANT SERVICE BY HOMOMORPHIC CRYPTOGRAPHY|

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US15/756,623| US10754907B2|2015-09-03|2016-09-01|Method for confidentially querying a location-based service by homomorphing cryptography|

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PCT/EP2016/070570| WO2017037151A1|2015-09-03|2016-09-01|Method for confidentially querying a location-based service by homomorphic cryptography|

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EP16784401.8A| EP3345175B1|2015-09-03|2016-09-01|Method for confidentially querying a location-based service by homomorphic cryptography|