FIELD OF THE INVENTION
The present invention relates to the field of 3D graphics. In particular, the present invention relates to a method and a device for encrypting a 3D object, and to a method and a device for decrypting a 3D object.
BACKGROUND
In 3D applications such as 3D worlds built for gaming, immersive or mixed reality, communication through avatars in virtual worlds and other types of socializing metaverses, producers of synthesized or scanned 3D content that have significant value look for ways to both protect these objects against unauthorized access or copy, but also to create an incentive for the users to pay in order to access such content in a legal and traceable manner. Since these objects are embedded in the 3D world or metaverse, one option could be to “show nothing” where the object should appear and keep the object in an encrypted format. However, if there is no sign that some valuable object is available in a given portion of the 3D world in case the user pays for it, it will be difficult for the user to find it and there will be no incentive for buying access to the enriched premium version of the metaverse. To this end, geometry-preserving cryptography has been proposed so far to solve this aspect of the problem: the 3D object is shuffled inside its bounding box (being contained in the same bounding box makes sure the scrambled object will not provoke intersections with other elements of the 3D world/metaverse) so that the 3D engine displays either a scrambled version of the object if the user did not pay for the premium access, or the deciphered object in case the user did pay for it.
Different geometry-preserving cryptography techniques for encrypting and decrypting a 3D object have been proposed. However, the known techniques do not provide a satisfactory solution to the following requirements:
- The ciphered object should not slow down the rendering speed of the 3D engine (too many faces flips or intersections can complicate the z-buffer management of the Graphic Processor Units), otherwise the application loses its interest.
- The decryption must have a low complexity so that it also does not slow down the 3D engine rendering the 3D world or socializing metaverse.
- The encryption should be secure enough so that a user cannot reconstruct the 3D model from a surface reconstruction attack.
- The 3D engine must be able to deal with the necessary secret keys and deciphering.
SUMMARY
It is thus an object of embodiments of the present invention to propose a method and a device for encrypting or decrypting a 3D object, which do not show the inherent shortcomings of the prior art.
Accordingly, embodiments relate to a method for encrypting a 3D object defined at least by a set of first points and a first set of faces, contained in a bounding box, the method being executed by an encryption device and comprising:
- determining a set of second points by bijection of the set of first points, and a second set of faces,
- determining an encrypted 3D object defined at least by the set of second points and the second set of faces,
wherein the first points are associated with respective first indexes, the second points are associated with respective second indexes, a face of the first set of faces is specified by a list of first indexes and a corresponding face of the second set of faces is specified by a list of corresponding second indexes,
wherein the encrypted 3D object is contained in said bounding box,
the method further comprising:
- partitioning the bounding box into a set of first sub-boxes,
- determining a set of second sub-boxes by bijection of the set of first sub-boxes, in function of a secret key,
wherein the position of a second point is determined in function the position of the corresponding first point, the position of the first sub-box containing the corresponding first point, and the position of the second sub-box corresponding with said first sub-box.
Correspondingly, embodiments relate to a device for encrypting a 3D object defined at least by a set of first points and a first set of faces, contained in a bounding box, comprising:
- means for determining a set of second points by bijection of the set of first points, and a second set of faces,
- means for determining an encrypted 3D object defined at least by the set of second points and the second set of faces,
wherein the first points are associated with respective first indexes, the second points are associated with respective second indexes, a face of the first set of faces is specified by a list of first indexes and a corresponding face of the second set of faces is specified by a list of corresponding second indexes,
wherein the encrypted 3D object is contained in said bounding box,
the device further comprising:
- means for partitioning the bounding box into a set of first sub-boxes,
- means for determining a set of second sub-boxes by bijection of the set of first sub-boxes, in function of a secret key,
wherein the position of a second point is determined in function the position of the corresponding first point, the position of the first sub-box containing the corresponding first point, and the position of the second sub-box corresponding with said first sub-box.
Embodiments also relate to a method for decrypting an encrypted 3D object defined at least by a set of second points and a second set of faces, contained in a bounding box, the method being executed by an decryption device and comprising:
- determining a set of third points by bijection of the set of second points, and a third set of faces,
- determining a decrypted 3D object defined at least by the set of third points and the third set of faces,
wherein the second points are associated with respective second indexes, the third points are associated with respective third indexes, a face of the second set of faces is specified by a list of second indexes and a corresponding face of the third set of faces is specified by a list of corresponding third indexes,
wherein the decrypted 3D object is contained in said bounding box,
the method further comprising:
- partitioning the bounding box into a set of second sub-boxes,
- determining a set of third sub-boxes by bijection of the set of second sub-boxes, in function of a secret key,
wherein the position of a third point is determined in function the position of the corresponding second point, the position of the second sub-box containing the corresponding second point, and the position of the third sub-box corresponding with said first sub-box.
Correspondingly, embodiments relate to a device for decrypting an encrypted 3D object defined at least by a set of second points and a second set of faces, contained in a bounding box, comprising:
- means for determining a set of third points by bijection of the set of second points, and a third set of faces,
- means for determining a decrypted 3D object defined at least by the set of third points and the third set of faces,
wherein the second points are associated with respective second indexes, the third points are associated with respective third indexes, a face of the second set of faces is specified by a list of second indexes and a corresponding face of the third set of faces is specified by a list of corresponding third indexes,
wherein the decrypted 3D object is contained in said bounding box,
the device further comprising:
- means for partitioning the bounding box into a set of second sub-boxes,
- means for determining a set of third sub-boxes by bijection of the set of second sub-boxes, in function of a secret key,
wherein the position of a third point is determined in function the position of the corresponding second point, the position of the second sub-box containing the corresponding second point, and the position of the third sub-box corresponding with said first sub-box.
Partitioning the bounding box into a set of first sub-boxes may comprise an octree decomposition of the bounding box.
The octree decomposition may be iterated until a predefined maximum decomposition level is reached or until the sub-boxes comprises at maximum one first point.
The position of a second point may be determined by one of the following displacement types:
- a translation of the corresponding first point according to the translation between a center of the first sub-box containing the corresponding first point and a center of the second sub-box corresponding with said first sub-box,
- a translation of the corresponding first point according to the translation between the center of the first sub-box containing the corresponding first point and the center of the second sub-box corresponding with said first sub-box, followed by a mirroring with respect to the center of said second sub-box,
- a rotation of the corresponding first point according to the rotation between the center of the first sub-box containing the corresponding first point and the center of the second sub-box corresponding with said first sub-box,
- a translation of the corresponding first point according to the translation between the center of the first sub-box containing the corresponding first point and the center of the second sub-box corresponding with the said first sub-box, followed by a mirroring of the points with respect to a medial plane of said second sub-box center.
The displacement type for determining a second point depends on the secret key.
Embodiments also relate to a computer program comprising instructions for performing one of the methods mentioned before when said instructions are executed by a computer.
BRIEF DESCRIPTION OF THE DRAWINGS
The above and other objects and features of the invention will become more apparent and the invention itself will be best understood by referring to the following description of embodiments taken in conjunction with the accompanying drawings wherein:
FIG. 1 is a flowchart of a method for encrypting a 3D object,
FIG. 2 is a functional view of a device for encrypting a 3D object,
FIG. 3 shows the decomposition of the bounding box of a 3D object into an octree, and the scrambling of the octree,
FIG. 4 is a flowchart of a method for decrypting a 3D object,
FIG. 5 is a functional view of a device for decrypting a 3D object, and
FIG. 6 is a structural view of a device for encrypting and/or decrypting a 3D object.
DESCRIPTION OF EMBODIMENTS
FIG. 1 is a flowchart of a method for encrypting a 3D object O into an encrypted 3D object O.
A 3D object O is defined at least by a set of points pi and a set of faces F (step 51). A point pi has an index i ranging for example from 1 to M, where M is the number of points pi, and is specified for example by its coordinates (xi, yi, zi). A face is defined by an ordered list of points pi, specified by their indexes i. The 3D object O may be defined also by additional data, such as texture, color . . .
The bounding box B of the 3D object O is the rectangular parallelepiped of minimum dimension within which all points pi are included. In order to encrypt the 3D object O, the bounding box B is partitioned in sub-boxes nj (step S2), and the encryption is based on a scrambling of the indexes j.
More precisely, in one embodiment illustrated on FIG. 3, the bounding box B is partitioned by octree decomposition. Initially, the bounding box B is equally subdivided along its three principal axes in eight octants, which correspond to eight sub-nodes of the octree. All the points pi contained in one octant are associated with the corresponding sub-node in the tree structure at the first decomposition level. For the next decomposition levels, the same decomposition approach is applied: an octant of the decomposition level l is partitioned in eight octants of the decomposition level l+1, and the points pi contained in one octant of the decomposition level l+1 are associated with the corresponding sub-node in the tree structure. The decomposition process continues until the decomposition level is equal to a predefined threshold maximum_decomposition_level, or the end sub-nodes of the octree contain at maximum one point pi.
At this stage, the octants of the last decomposition level define a partitioning of the bounding box B in sub-boxes. The sub-nodes of the octree and the corresponding sub-boxes are denoted n1, with the index j ranging from 1 to 23L (or 0 to 23L−1) where L is the last decomposition level. The indexes j are assigned for example by rastering first along the x axis, then the y axis, and then the z axis. The points pi are associated with the node nj corresponding to the sub-box within which they are located.
Then, the indexes j are scrambled in function of a pseudo random number generator controlled by a secret key k, such that each input index j is associated with one and only one output index sj (i.e. a bijection) different from j. Spatially, this correspond to permuting the sub-boxes n1 to determine another set of sub-boxes nsj, by a bijection which depends on the secret key k (step S3):
n
s
j
=f(nj, k).
Then, point and faces for the encrypted 3D object Os are determined (step S4). For this, the points pi are displaced according to the displacement of the sub-box nj within which they are contained to the corresponding sub-box nsj. The displaced points are denoted psi and are associated to the points pi by a bijection. The indexes of the points psi may be equal to the indexes of the points pi:si=i. In that case, the set of faces Fs of the encrypted 3D object Os is equal to the set of faces F of the 3D object O: Fs=F. Alternatively, the indexes of the points psi may be a permutation of the indexes of the corresponding points pi. In that case, the indexes of the set of faces Fs are adapted correspondingly. In both cases, a face of the set of faces F is specified by a list of indexes i and a corresponding face of the set of faces Fs is specified by a list of corresponding second indexes si.
The displacement may be done in different ways. Options are:
- Type A: to perform a simple translation of the points pi according to the translation that the center of the sub-box nj undergoes between its original position and its scrambled position (the position of the corresponding sub-node nsj). For a point pi ∈ R3 associated to the original node nj, the scrambled position of this point is noted psi and is given by:
∀pi∈nj, psi=pi+{right arrow over ((nsj−nj))}
- Type B: to perform a simple translation of the points pi according to the translation that the center of the sub-box nj undergoes between its original position and its scrambled position (the position of the corresponding sub-node nsj), followed by a mirroring of the points with respect to their sub-box center so that normals would still point outwards of the bounding box. For each point pi associated to the original node nj, the scrambled position of this point (associated now to the scrambled position of node nj noted now nsj) is noted psi and is given by:
∀pi∈nj, psi=pi+{right arrow over ((nsj−nj))}−2·{right arrow over ((pl−nj))}
- Type C: to rotate the points pi in the same way as the center of the sub-box nj is rotated between its original position and its scrambled position. For each point pi associated to the original node nj, the scrambled position of this point (associated now to the scrambled position of node nj noted now nsj) is noted psi and is given by:
∀pi∈nj, psi=Aspi,
- where As is the rotation matrix obtained when rotating the vector {right arrow over (Onj)} towards {right arrow over (Onsj)}, where O is the center of the object bounding box.
- Type D: to perform a simple translation of the points pi according to the translation that the center of the sub-box nj undergoes between its original position and its scrambled position, followed by a mirroring of the points with respect to one of the medial planes of the sub-box center: Types Dx, Dy and Dz if the plane is orthogonal to the x, y and z axis respectively (in world coordinates of the bounding box). For each point pi associated to the original node nj, the scrambled position of this point (associated now to the scrambled position of node nj noted now nsj) is noted psi and is given by:
∀pi∈nj, psi=pi+{right arrow over ((nsj−nj))}−2·{right arrow over ((pl−pl·Dx))}
- where pi·Dx stands for the orthogonal projection of point pi on medial plane Dx.
For each sub-box n1, one of the displacement type is selected. For example, the choice of the displacement option (Type A, B, C or D) depends on the secret key k.
The resulting set of points psi and set of faces F, define (at least partially) the encrypted 3D object Os (step S5).
The encrypted 3D object Os is contained in the same bounding box B and may therefore by displayed in a 3D world without interfering with other objects. Displaying the encrypted 3D object Os give an incentive to obtain the decrypted 3D object, for example by buying the usage right and obtaining the secret key k.
Moreover, the displacement of the points pi contained in the same sub-box nj is performed in the same manner. If the maximum level of decomposition is small, then large group of points pi are clustered and shuffled in the same way in the 3D space, which reduces triangle intersections and therefore rendering complexity of the encrypted 3D object Os and its deciphering complexity. If the maximum subdivision step is taken as such that maximum one point pi is contained in each sub-box nj, then the security against surface reconstruction attack is high. More, in any case it does not rely on point indexes for its security. The selection of an intermediate threshold for octree maximum subdivision steps provide a good trade-off between security and complexity.
FIG. 2 shows an encrypting device 1 for encrypting a 3D object O. The encrypting device 1 executes the method of FIG. 1 and comprises an octree decomposition module 2, a pseudo random number generator 3 and an octree scrambling module 4.
The octree decomposition module 2 partitions the bounding box B of the 3D object O into sub-boxes nj. The partitioning is based on octree decomposition as explained with respect to step S2 of FIG. 1.
The pseudo random number generator 3 is controlled by the secret key k and determines pseudo random number.
The octree scrambling module 4 scrambles the nodes of the octree in function of the output of the pseudo random number generator 3, as explained with respect to step S3 of FIG. 1, and displaces the points pi based on the scrambling of the nodes as explained with respect to step S4 of FIG. 1.
The output of the octree scrambling module 4 is the encrypted 3D object Os.
FIG. 3 illustrates the method of FIG. 1 for a simple example where maximum _decomposition_level=1. Part (a) shows the bounding box B of a 3D object partitioned in an octree of eight nodes n0 to n7, and points pi. Part (b) shows the bounding box B of the encrypted 3D object Os partitioned in an octree of eight nodes ns0 to ns7, and points psi. In this example, the points pi are displaced by a simple translation according to the octree node scrambling, i.e. displacement of type A. The scrambling of the nodes used in this example is shown on part (c)
Accordingly, points p1 and p2 of the original object contained in node n0 are translated to points ps1and ps2 of the encrypted object, contained in node ns5. Similarly, point p3 of the original object contained in node n2 is translated to point ps3 of the encrypted object, contained in node ns1. The object appearance is significantly changed while still contained into its bounding box B. A face of the original 3D object O, defined by points p1, p2 and p3, correspond to a face defined by points ps1, ps2 and ps3 in the encrypted 3D object Os. Since p1 and p2 are translated together according to the displacement from node n0 to ns5, intersections with other faces are limited and rendering complexity of the encrypted 3D object Os is limited.
FIG. 4 is a flowchart of a method for decrypting an encrypted 3D object O, into an decrypted 3D object Ou.
The encrypted 3D object Os has been obtained by encrypting a 3D object O with a secret key k, according to the method of FIG. 1, and is defined at least by a set of points psi and a set of faces F (step S6). The encrypted 3D object Os may be defined also by additional data, such as texture, color . . .
The bounding box B of the encrypted 3D object Os is the rectangular parallelepiped of minimum dimension within which all points psi are included. It is the same as the bounding box B of the 3D object O. In order to decrypt the encrypted 3D object Os, the bounding box B is partitioned in sub-boxes nsj (step S7), and the decryption is based on a descrambling of the indexes
More precisely, the bounding box B is partitioned by octree decomposition in the same manner as in step S2 of FIG. 1. At the end, the octants of the last decomposition level define a partitioning of the bounding box B in sub-boxes. The sub-nodes of the octree and the corresponding sub-boxes are denoted nsj. The points psiare associated with the node nsj corresponding to the sub-box within which they are located.
It should be noted that, whether partitioning the bounding box B stops at the threshold maximum_decomposition_level or when the sub-nodes are associated with at maximum one point psi, the partitioning will be the same as the one of step S2. Consequently, by descrambling the indexes sj in function of the same pseudo random number generator as for encrypting, controlled by the secret key k, indexes uj are obtained which correspond to the indexes j of the decomposition of the original 3D object O. Spatially, this correspond to permuting the sub-boxes nsj to determine another set of sub-boxes nuj, by a bijection which depends on the secret key k (step S8):
n
u
j
=f(nsj, k).
Then, point and faces for the decrypted 3D object Ou are determined (step S9). For this, the points psi are displaced according to the displacement of the sub-box nsj within which they are contained to the corresponding sub-box nuj. The displaced points are denoted pui and are associated to the points psi by a bijection. The indexes of the points pui may be equal to the indexes of the points psi:ui=si. In that case, the set of faces Fu of the decrypted 3D object Ou is equal to the set of faces Fs of the encrypted 3D object Os: Fu=Fs. Alternatively, the indexes of the points pui may be a permutation of the indexes of the corresponding points psi. In that case, the indexes of the set of faces Fu are adapted correspondingly. In both cases, a face of the set of faces Fs is specified by a list of indexes si and a corresponding face of the set of faces Fu is specified by a list of corresponding second indexes ui.
The displacement types correspond to the types used for encryption:
- Type A: Noting nuj the unscrambled position of scrambled node nsj, which is the same as the original node nj if the correct secret key k is used for de-scrambling, unscrambling positions of the scrambled points psi ∈ nsj are given by:
∀psi∈nsj, pui=psi+{right arrow over ((nuj−nsj))}
- Type B: unscrambling positions of the scrambled points psi ∈ nsj are given by:
∀psi∈nsj, pui=psi+{right arrow over ((nuj−nsj))}−2·{right arrow over ((psl −nsj))}
- Type C: unscrambling positions of the scrambled points psi ∈ nsj are given by:
∀psi∈nsj, pui=Aupsi
- where Au is the rotation matrix obtained when rotating the vector {right arrow over (Onsj )} towards {right arrow over (Onuj)}, where O is the center of the (scrambled) object bounding box.
- Type D: unscrambling positions of the scrambled points psi ∈ nsj are given by:
∀pi∈nj, pui=psi+{right arrow over ((nuj−nsj))}−2·{right arrow over ((psl−psl·Dsx))}
- where psi·Dsx stands for the orthogonal projection of point psi on the scrambled medial plane Dsx.
For each sub-box nsj, one of the displacement type is selected. For example, the choice of the displacement option (Type A, B, C or D) depends on the secret key k.
The resulting set of points pui set of faces Fu define (at least partially) the decrypted 3D object Ou (step S10), which is equal to the original 3D object O if the correct secret key k was used.
Thus, decrypting the encrypted 3D object Os is based on octree decomposition and descrambling, and has a low complexity for low decomposition level as explained before.
FIG. 5 shows a decrypting device 5 for decrypting a 3D object Os. The decrypting device 5 executes the method of FIG. 4 and comprises an octree decomposition module 6, a pseudo random number generator 7 and an octree descrambling module 8. The functioning of the octree decomposition module 6, the pseudo random number generator 7 and the octree descrambling module 8 correspond to that of the corresponding module of FIG. 2.
The output of the octree descrambling module 8 is the decrypted 3D object Ou.
The embodiment described above uses octree decomposition. This has the advantage that, provided that the encrypting device 1 and the decrypting device 5 use the same maximum_decomposition_level threshold, the decomposition of the bounding box of the encrypted 3D object Os by the decrypting device 5 corresponds to the decomposition of the bounding box of the original 3D object O by the encrypting device 1. For this, the decrypting device 5 does not need to obtain data related to the decomposition performed by the encrypting device 1. In other words, the decomposition is implicit. Accordingly, descrambling and displacing the points based on the same secret key k allows determining the decrypted 3D object Ou equal to the original 3D object O, without the need of decomposition data.
However, in other embodiments, other points clustering techniques may be used for partitioning the bounding box of the original 3D object O into sub-boxes. In some case, the decrypting device 5 may need to obtain decomposition data specifying the decomposition of the bounding box of the original 3D object O by the encrypting device 1, for example parameters, for decomposing the bounding box of the encrypted 3D object Os in the corresponding manner. This can be done by so-called “side-information” that is received together with the secret key.
FIG. 6 is a structural view of a device, which may be the encrypting device 1 and/or the decrypting device 5. The device of FIG. 6 comprises a processor 10 and a memory 11. The memory comprises a computer program P which include instructions executable by the processor 10. The functional modules shown on FIG. 2 or 5 may correspond to the execution of the computer program P by the device of FIG. 6.
It is to be remarked that the functions of the various elements shown in the figures may be provided through the use of dedicated hardware as well as hardware capable of executing software in association with appropriate software. When provided by a processor, the functions may be provided by a single dedicated processor, by a single shared processor, or by a plurality of individual processors, some of which may be shared, for example in a cloud computing architecture. Moreover, explicit use of the term “processor” should not be construed to refer exclusively to hardware capable of executing software, and may implicitly include, without limitation, digital signal processor (DSP) hardware, network processor, application specific integrated circuit (ASIC), field programmable gate array (FPGA), read only memory (ROM) for storing software, random access memory (RAM), and non volatile storage. Other hardware, conventional and/or custom, may also be included. Their function may be carried out through the operation of program logic, through dedicated logic, through the interaction of program control and dedicated logic, or even manually, the particular technique being selectable by the implementer as more specifically understood from the context.
It should be further appreciated by those skilled in the art that any block diagrams herein represent conceptual views of illustrative circuitry embodying the principles of the invention. Similarly, it will be appreciated that any flow charts represents various processes which may be substantially represented in computer readable medium and so executed by a computer or processor, whether or not such computer or processor is explicitly shown.
Embodiments of the method can be performed by means of dedicated hardware and/of software or any combination of both.
While the principles of the invention have been described above in connection with specific embodiments, it is to be clearly understood that this description is made only by way of example and not as a limitation on the scope of the invention, as defined in the appended claims.
Patent Application
20170169606
