Abstract:
A physical unclonable function (PUF) imaged through two faces is disclosed. The PUF is difficult to counterfeit because the view through both faces must be duplicated for a successful counterfeit. PUF may be incorporated into a user-replaceable supply item for an imaging device. A PUF reader may be incorporated into an imaging device to read the PUF. Other systems and methods are disclosed.

Description:
CROSS REFERENCES TO RELATED APPLICATIONS 
       [0001]    The following applications are related and were filed contemporaneously with this application: “PHYSICAL UNCLONABLE FUNCTIONS HAVING MAGNETIC AND NON-MAGNETIC PARTICLES”, “METHODS OF MAKING PHYSICAL UNCLONABLE FUNCTIONS HAVING MAGNETIC AND NON-MAGNETIC PARTICLES”, “ROTATING MAGNETIC MEASUREMENTS OF PHYSICAL UNCLONABLE FUNCTIONS”, “ROTATING IMAGE MEASUREMENTS OF PHYSICAL UNCLONABLE FUNCTIONS”, “ROTATING POLARIZATION MEASUREMENTS OF PHYSICAL UNCLONABLE FUNCTIONS”. 
       BACKGROUND 
       [0002]    1. Field of the Disclosure 
         [0003]    The present disclosure relates generally to anti-counterfeit systems and more particularly to physical unclonable functions. 
         [0004]    2. Description of the Related Art 
         [0005]    Counterfeit printer supplies, such as toner bottles, are a problem for consumers. Counterfeit supplies may perform poorly and may damage printers. Printer manufacturers use authentication systems to deter counterfeiters. Physical unclonable functions (PUF) are a type of authentication system that implements a physical one-way function. Ideally, a PUF cannot be identically replicated and thus is difficult to counterfeit. Thus, it is advantageous to maximize the difficulty of replicating a PUF to deter counterfeiters. It is also advantageous for the PUF and PUF reader to be to cost. 
       SUMMARY 
       [0006]    The invention, in one form thereof, is directed to a system having a body; a non-opaque substrate mounted to the body containing a plurality of particles dispersed in the substrate within a cubic region having a first face and a second face, the first face is contiguous with the second face; and a non-volatile memory device mounted to the body containing first image data of the particles as viewed through the first face while the cubic region is illuminated through the second face and second image data of the particles as viewed through the second face while the cubic region is illuminated through the first face. 
         [0007]    The invention, in another form thereof, is directed to a system having a body; a non-opaque substrate mounted to the body containing a plurality of particles dispersed in the substrate within a cubic region having a first face and a second face, the first face is contiguous with the second face; and a non-volatile memory device mounted to the body containing first image data of the particles as viewed simultaneously through the first face and the second face while the cubic region is illuminated through the second face and second image data of the particles as viewed simultaneously through the first face and the second face while the cubic region is illuminated through the first face. 
         [0008]    The invention, in yet another form thereof, is directed to a method of manufacturing an authentication device including attaching a non-volatile memory device to a body; attaching a non-opaque substrate to the body containing a plurality of particles dispersed in the substrate within a cubic region having a first face and a second face, the first face is contiguous with the second face; generating first image data of the particles as viewed through the first face while the cubic region is illuminated through the second face and is not illuminated through the first face; generating second image data of the particles as viewed through the second face while the cubic region is illuminated through the first face and is not illuminated through the second face; generating encrypted image data by encrypting the first image data and the second image data; and writing the encrypted image data to the non-volatile memory device. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0009]    The accompanying drawings incorporated in and forming a part of the specification, illustrate several aspects of the present disclosure, and together with the description serve to explain the principles of the present disclosure. 
           [0010]      FIG. 1  is a block diagram of an imaging system including an image forming device according to one example embodiment. 
           [0011]      FIG. 2  is an orthogonal view of a substrate containing magnetic and non-magnetic particles. 
           [0012]      FIG. 3  is a view of a PUF mounted to a body. 
           [0013]      FIG. 4  is a side view of a PUF and PUF readers. 
           [0014]      FIG. 5  is a view of a cylindrical PUF. 
           [0015]      FIG. 6  is a view of a PUF and locations along a circular path. 
           [0016]      FIG. 7  is a series of data elements corresponding to a sequential series of locations along a circular path. 
           [0017]      FIG. 8  is a side view of a PUF mounted to a body. 
           [0018]      FIG. 9  is a view of a PUF and a non-circular path. 
           [0019]      FIG. 10  and  FIG. 11  are orthogonal views of a PUF and sensors. 
           [0020]      FIG. 12  is an orthogonal view of a PUF mounted to a body. 
           [0021]      FIG. 13 ,  FIG. 14 , and  FIG. 15  are flowcharts of methods of making security devices. 
           [0022]      FIG. 16  is a side view of PUF and a PUF reader. 
       
    
    
     DETAILED DESCRIPTION 
       [0023]    In the following description, reference is made to the accompanying drawings where like numerals represent like elements. The embodiments are described in sufficient detail to enable those skilled in the art to practice the present disclosure. It is to be understood that other embodiments may be utilized and that process, electrical, and mechanical changes, etc., may be made without departing from the scope of the present disclosure. Examples merely typify possible variations. Portions and features of some embodiments may be included in or substituted for those of others. The following description, therefore, is not to be taken in a limiting sense and the scope of the present disclosure is defined only by the appended claims and their equivalents. 
         [0024]    Referring to the drawings and particularly to  FIG. 1 , there is shown a block diagram depiction of an imaging system  50  according to one example embodiment. Imaging system  50  includes an image forming device  100  and a computer  60 . Image forming device  100  communicates with computer  60  via a communications link  70 . As used herein, the term “communications link” generally refers to any structure that facilitates electronic communication between multiple components and may operate using wired or wireless technology and may include communications over the Internet. 
         [0025]    In the example embodiment shown in  FIG. 1 , image forming device  100  is a multifunction device (sometimes referred to as an all-in-one (AIO) device) that includes a controller  102 , a user interface  104 , a print engine  110 , a laser scan unit (LSU)  112 , one or more toner bottles or cartridges  200 , one or more imaging units  300 , a fuser  120 , a media feed system  130  and media input tray  140 , and a scanner system  150 . Image forming device  100  may communicate with computer  60  via a standard communication protocol, such as, for example, universal serial bus (USB), Ethernet or IEEE 802.xx. Image forming device  100  may be, for example, an electrophotographic printer/copier including an integrated scanner system  150  or a standalone electrophotographic printer. 
         [0026]    Controller  102  includes a processor unit and associated memory  103  and may be formed as one or more Application Specific Integrated Circuits (ASICs). Memory  103  to may be any volatile or non-volatile memory or combination thereof such as, for example, random access memory (RAM), read only memory (ROM), flash memory and/or non-volatile RAM (NVRAM). Alternatively, memory  103  may be in the form of a separate electronic memory (e.g., RAM, ROM, and/or NVRAM), a hard drive, a CD or DVD drive, or any memory device convenient for use with controller  102 . Controller  102  may be, for example, a combined printer and scanner controller. 
         [0027]    In the example embodiment illustrated, controller  102  communicates with print engine  110  via a communications link  160 . Controller  102  communicates with imaging unit(s)  300  and processing circuitry  301  on each imaging unit  300  via communications link(s)  161 . Controller  102  communicates with toner cartridge(s)  200  and non-volatile memory  201  on each toner cartridge  200  via communications link(s)  162 . Controller  102  communicates with fuser  120  and processing circuitry  121  thereon via a communications link  163 . Controller  102  communicates with media feed system  130  via a communications link  164 . Controller  102  communicates with scanner system  150  via a communications link  165 . User interface  104  is communicatively coupled to controller  102  via a communications link  166 . Processing circuitry  121  and  301  may include a processor and associated memory such as RAM, ROM, and/or non-volatile memory and may provide authentication functions, safety and operational interlocks, operating parameters and usage information related to fuser  120 , toner cartridge(s)  200  and imaging unit(s)  300 , respectively. Controller  102 . processes print and scan data and operates print engine  110  during printing and scanner system  150  during scanning. 
         [0028]    Computer  60 , which is optional, may be, for example, a personal computer, including memory  62 , such as RAM, ROM, and/or NVRAM, an input device  64 , such as a keyboard and/or a mouse, and a display monitor  66 . Computer  60  also includes a processor, input/output (I/O) interfaces, and may include at least one mass data storage device, such as a hard drive, a CD-ROM and/or a DVD unit (not shown). Computer  60  may also be a device capable of communicating with image forming device  100  other than a personal computer such as, for example, a tablet computer, a smartphone, or other electronic device. 
         [0029]    In the example embodiment illustrated, computer  60  includes in its memory a software program including program instructions that function as an imaging driver  68 , e.g., printer/scanner driver software, for image forming device  100 . Imaging driver  68  is in communication with controller  102  of image forming device  100  via communications link  70 . Imaging driver  68  facilitates communication between image forming device  100  and computer  60 . One aspect of imaging driver  68  may be, for example, to provide formatted print data to image forming device  100 , and more particularly to print engine  110 , to print an image. Another aspect of imaging driver  68  may be, for example, to facilitate the collection of scanned data from scanner system  150 . 
         [0030]    In some circumstances, it may be desirable to operate image forming device  100  in a standalone mode, In the standalone mode, image forming device  100  is capable of functioning without computer  60 . Accordingly, all or a portion of imaging driver  68 , or a similar driver, may be located in controller  102  of image forming device  100  so as to accommodate printing and/or scanning functionality when operating in the standalone mode. 
         [0031]    Several components of the image forming device  100  are user replaceable e.g. toner cartridge  200 , fuser  120 , and imaging unit  300 . It is advantageous to prevent counterfeiting these user replaceable components. A PUF  202  may be attached to the toner cartridge  200  to prevent counterfeiting as described below. A PUF reader  203  may be integrated into the image forming device  100  to verify the authenticity of the PUF  202 . Data related to the PUF  202  may reside in non-volatile memory  201 . 
         [0032]      FIG. 2  shows a region of a substrate  210  containing, for example, transparent plastic. Dispersed in the substrate are a plurality of non-magnetic particles  212  and magnetic particles  214 . The particles are distributed randomly such that it is extremely difficult to reproduce the exact distribution and alignment of particles. Thus, the substrate  210  and the particles form a PUF. It is preferable to use both magnetic and non-magnetic particles in a PUF to increase the difficulty in fooling a PUF reader, since both magnetic and non-magnetic information would need to be counterfeited. Further, it is lower cost to make non-magnetic particles vs. magnetic particles, so a mixture will be cheaper than an equivalent number of only magnetic particles. Also, in some practical PUF readers, it is preferred to use larger particles for image data and smaller magnetic particles for magnetic field data due to the resolution of the respective detectors. 
         [0033]      FIG. 3  shows an embodiment of a PUF. The substrate is in the form of a gear  310  containing a mixture of magnetic particles  214  and non-magnetic particles  212 , for example, the region of the substrate  210  is typical of the entire gear  310 . The gear  310  is configured to rotate about a shaft  312  located at the axis of rotation of the gear  310 . A raised collar  314  encircles the shaft  312  and is integrated with the gear  310 . The gear  310  has a plurality of teeth  316  configured to engage with a coupling  318  such that rotation of the coupling  318  causes the gear  310  to rotate about the shaft  312 . 
         [0034]    The gear  310  is mounted to a body  320  via the shaft  312 . A printed circuit board (PCB)  322  is also mounted to the body and contains a non-volatile memory  324  connected to a plurality of contacts  326 . The contacts  326  are used by a PUF reader to provide electrical connection to the non-volatile memory  324 . The coupling  318  is also mounted to the body  320  and contains a slot  328  used by the PUF reader to couple to the coupling  318 . Of course, other interface geometries may be used instead of a slot  328 . 
         [0035]    The non-volatile memory  324  contains field data corresponding to the magnetic field generated by the magnetic particles  214  as measured along a first circular path  330  centered on the axis of rotation of the gear  310 . The first circular path  330  has a radius  332 . The non-volatile memory  324  also contains image data of the magnetic particles  214  and non-magnetic particles  212  as viewed from the first circular path  330 . 
         [0036]    Note that paths that approximate a circular path may be equivalent to a circular path if the resulting measurements are equivalent to measurements taken along a circular path. For example, wobble in the rotation of the gear  310  may cause deviation from a pure circular path that will generate data that is accepted by a PUF reader as authentic. 
         [0037]      FIG. 4  shows a side of the gear  310 . The teeth  316  are omitted in this view for clarity.  FIG. 4  also shows a magnetic field sensor  410 , an image sensor  412 , a first illumination source  422 , and a second illumination source  426 , all located in the PUF reader. The magnetic field sensor  410  is located at a distance  418  from the axis  420  of rotation of the gear  310 . This distance  418  is the same as the radius  332  of the first circular path  330 . The image sensor  412  is located at a distance  419  from the axis  420  and is also the same as the radius  332  of the first circular path  330 . 
         [0038]    The field data in the non-volatile memory  324  was measured, for example, by the magnetic field sensor  410  and then written to the non-volatile memory  324 . The field data may be computationally adjusted for more efficient computation and comparison before written to the non-volatile memory  324 . For example, the field data may be clipped such that measurements below a clip threshold are set to a clip value e.g. set to zero. The magnetic field sensor may, for example, measure the magnetic field in one, two, or more orthogonal directions. Measurements in multiple directions are harder to counterfeit than measurements taken in a single direction. Measurements in a first direction may be used to determine when to clip measurements in a second direction e.g. if, at a given position along a path, the measured magnetic field in a first direction is less than a clip value the field data written to the non-volatile memory  324  corresponding to that position will be set to a clip value for both the first direction and for the second orthogonal direction. This may provide more uniform clipping and may make the PUF reader more repeatable. 
         [0039]    The image data in the non-volatile memory  324  was measured, for example, by the image sensor  412  and then written to the non-volatile memory  324 . The image data may be computationally adjusted before written to the non-volatile memory  324 . The image sensor  412  may be, for example, a point sensor, a linear array of point sensors, a two dimensional array of point sensors, etc. The image data may be generated by illuminating the particles with a first illumination source  422  with light traveling along a first illumination line  424  and then illuminating the particles with a second illumination source  426  using a second illumination line  428 . The first illumination line  424  is not the same as the second illumination line  428  such that differences in the rotation of individual particles will result in different image data generated by each illumination source. Thus, a counterfeit would need to reproduce the rotation of each particle. Preferably, some of the particles are flakes having an average thickness that is less than their average diameter to increase the contrast between image data generated by the two illumination sources. As used herein, average refers to number average. For example, average diameter is obtained by summing up the diameters of each particle in a set of particles and then dividing by the number of particles. Some particles may be excluded from a set such as, for example, particles with diameters less than 25 microns. 
         [0040]    The field data may be measured while rotating the gear  310  next to a stationary magnetic field sensor  410 , by moving the magnetic field sensor  410  next to a stationary gear  310 , etc. Similarly, the image data may be measured while rotating the gear  310  next to a stationary image sensor  412 , by moving the image sensor  412  next to a stationary gear  310 , etc. The field data and the image data may be measured at the same time, measured sequentially, etc. The non-volatile memory  324  may contain field data, image data, or both field data and image data. 
         [0041]    The non-volatile memory  324  may contain field data, image data or both field data and image data from more than one path, such as, for example, a second circular path  334  that encloses the first circular path  330 . Multiple paths may be stored to allow for variability in the position of sensors in a PUF reader. 
         [0042]    The non-volatile memory  324  may contain polarization data related to the angle of polarization of light passed through the gear  310 , in addition to or instead of field data and image data. The polarization may be caused by stress-induced birefringence in the gear material, which may contain, for example, polystyrene, polycarbonate, etc. The birefringence modulates the angle of polarization of light passed through regions of the gear  310 . The polarization data may correspond to measurements made along a path that encloses axis  420 . Birefringence may be caused by the presence of magnetic particles  214 , non-magnetic particles  212 , circular or non-circular holes in the gear  310  that create stress due to non-uniform cooling during the manufacturing process, etc. 
         [0043]      FIG. 16  shows a side view of the gear  310  and a PUF reader that measures light polarization.  FIG. 16  also shows a first light sensor  1610 , a second light sensor  1612 , an illumination source  1614 , and a beam splitter  1616 , all located in the PUF reader. The beam splitter  1616  is located at a distance  1618  from the axis  420  of rotation of the gear  310 . This distance  1618  is the same as the radius  332  of the first circular path  330 . Light from the illumination source  1614  passes through a first linear polarizing filter  1620 , through the gear  310 , and into the beam splitter  1616 . The light then simultaneously passes through a second linear polarizing filter  1622  to the first light sensor  1610  and though a third linear polarizing filter  1624  to the second light sensor  1612 . The second linear polarizing filter  1622  is rotated relative to the third linear polarizing filter  1622 , preferably ninety degrees. Thus, the first light sensor  1610  will measure a different polarity of light than the second light sensor  1612 . Birefringence modulates the angle of polarization of light passed through regions of the gear  310  as described above. It is preferable to measure transmitted light at two polarization angles to avoid a counterfeiter fooling the PUF reader with a varyingly opaque substrate, since both polarization angle sensors would measure the same opacity. Note that the first linear polarizing filter  1620  is optional depending on the properties of the illumination source  1614 . 
         [0044]      FIG. 5  shows an alternative substrate configuration. The substrate is a cylinder having an axis of rotation  512 . Field data and image data may be measured along a circular path  514  located around the side of the cylinder  510  and centered on the axis  512 . 
         [0045]      FIG. 6  shows a first location  610  and a second location  612  on the first circular path  330 . In this example, the magnetic field sensor  410  is positioned at the first location  610  and the image sensor  412  is positioned at the second location  612 . Alternatively, the magnetic field sensor  410  may be positioned at the first location  610  and the beam splitter  1616  may be positioned at the second location  612 . Preferably, the sensors are not positioned at the same location to reduce system complexity, The central angle  614  between the first location  610  and the second location  612  is greater than 45 degrees to provide sufficient space for the sensors. 
         [0046]      FIG. 7  shows a series of data elements corresponding to a sequential series of locations along the first circular path  330 . The field data elements are stored sequentially in the non-volatile memory device  324  as are the image data elements. In this example, there are forty field data elements F0-F39 spaced 10 degrees apart. For simplicity,  FIG. 7  shows a subset of these data elements. The central angle is 90 degrees, and 0 degrees is assigned to the first location  610 . It is preferable to take measurements from both sensors at the same time to improve system throughput. Thus, since the first field data element  710  is at zero degrees, the first image data element  712  is at 90 degrees. There are forty image data elements I0-I39 that are also spaced 10 degrees apart. Of course, more or fewer data elements may be used and the spacing need not be uniform. In operation, the PUF reader will simultaneously measure magnetic field data and image data and thus the physical offset between the first location  610  and second location  612  is encoded in the data. 
         [0047]    It is preferable to have at least 360 degrees of field data and image data so that the PUF reader may start reading at any position along a path. With this system, an absolute position indicator is not required e.g. an one-per-revolution sensor. Note that the field data in  FIG. 7  corresponds to more than 360 degrees around the first circular path  330 . The overlapping data removes the discontinuity between the first reading at, for example, 0 degrees and the last reading at 350 degrees. The discontinuity may be caused by, for example, wobble in the gear. The PUF reader may average the reading at 0 degrees and the reading at 360 degrees to reduce this error. 
         [0048]    Measuring field data and image data around a closed path is superior to measuring along a linear path. Multiple passes may be easily measured to tune sensor dynamic range, average readings to reduce noise, etc. Also, it is easier, and thus cheaper, to precisely control rotational motion than linear motion because fewer mechanical tolerances contribute to position inaccuracy. 
         [0049]      FIG. 8  shows a side view of the gear  310  and the body  320 . The shaft  312  protrudes beyond the gear  310  on the side  810  opposite the body. The PUF reader may set the position of the sensors by using the side of the shaft as a datum. This will improve the positioning tolerance of the system. Alternatively, the PUF reader may use the side of the raised collar  314  as a datum. As shown in  FIG. 9 , if the raised collar  914  is non-circular, the resulting path  930  will also be non-circular and will follow the outer surface of the raised collar  914  at a fixed offset. A non-circular path may be more difficult to counterfeit than a simpler circular path. Alternatively, the raised collar may be circular with a center that is offset from the shaft  912 , resulting in a circular path that is not centered on the axis of rotation of the gear  910 . 
         [0050]      FIG. 10  shows a cubic region  1000  of a non-opaque substrate  1002  containing a plurality of particles  1004 . The cubic region  1000  has a first face  1006  that is contiguous with a second face  1008 . The first face  1006  and the second face  1008  may be surfaces of the substrate  1002 . Alternatively, the first face  1006  and the second face  1008  may be faces of a cubic region within a larger substrate. The particles may be reflective, opaque, magnetic, and any combination thereof. Preferably, each particle has a diameter greater than 100 microns and the average diameter of the particles is between 200 and 2000 microns inclusive so the particles are large enough to be viewable by low-cost image sensors while being small enough to provide sufficient complexity to defeat counterfeiters. Note that the diameter of a non-spherical particle is the diameter of the smallest sphere that encloses the particle. Ideally, the substrate is composed of a transparent material such as transparent plastic. A reflective particle has a specular reflection that is at least twice as large as its diffuse reflection. 
         [0051]    The cubic region  1000  may be used as a PUF. A PUF reader contains a first image sensor positioned to view the particles through the second face  1008  while a first illumination source  1012  illuminates the particles through the first face  1006  to measure first image data. The first illumination source  1012  is positioned relative to the first face  1006  to minimize any surface reflections bouncing off the first face  1006  and striking the first image sensor  1010 . In this example, the first illumination source  1012  is pointed orthogonally at the first face  1006 . A second image sensor  1014  is positioned to view the particles through the first face  1006  while a second illumination source  1016  illuminates the particles through the second face  1008  to measure second image data. The PUF reader compares the first image data and the second image data to a master database to verify the authenticity of the PUF. The master database may be stored on a computer server, on a non-volatile memory associated with the PUF, etc. Preferably, the first illumination source  1012  and the second illumination source  1016  are not energized simultaneously to avoid surface reflections corrupting the image data. 
         [0052]      FIG. 11  shows an alternative PUF reader configuration. A first mirror  1102  and a second mirror  1104  simultaneously reflect images of the particles from the first face  1006  and the second face  1008  respectively to an image sensor  1106 . In operation, the first illumination source  1012  illuminates the particles through the first face  1006  and the image sensor  1106  measures first image data of the particles as viewed simultaneously through the first face  1006  and the second face  1008 . The second illumination source  1016  illuminates the particles through the second face  1008  and the image sensor  1106  measures second image data of the particles as viewed simultaneously through the first face  1006  and the second face  1008 . This configuration requires a single image sensor and thus may be lower cost than a configuration that requires multiple image sensors. In this example, the first illumination source  1012  and the second illumination source  1016  are not energized simultaneously so that the first image data is different than the second image data. However, third image data may be generated by energizing both the first illumination source  1012  and the second illumination source  1016  simultaneously. 
         [0053]      FIG. 12  shows the substrate  1002  mounted to a body  1202 . Also mounted to the body  1202  is a non-volatile memory  1204  mounted on a PCB  1206  having electrical contacts  1208 . The non-volatile memory  1204  contains one or more of the image data described above with respect to  FIG. 10  and  FIG. 11 . In operation, a PUF tester will measure image data of the particles in the substrate  1002  to compare with the image data in the non-volatile memory  1204 . If the image data matches, the PUF is genuine otherwise the PUF is a counterfeit. Preferably, the image data in the non-volatile memory  1204  is measured and stored after the substrate  1002  is mounted to the body  1202  so any image distortion caused by reflections off the body will occur in both the non-volatile memory image data and the image data. measured by the PUF tester. 
         [0054]      FIG. 13  shows an example embodiment of a method of making a security device according to one embodiment. Method  1300  makes a PUF that is suitable for both magnetic field measurements and image measurements and is thus difficult to counterfeit. 
         [0055]    At block  1302 , a carrier having a volume of X, magnetizable particles having a volume Y, and non-magnetizable particles having a volume Z are mixed. Preferably, 0.25*X&gt;Y&gt;0.000005*X and 0.5*X&gt;Z&gt;0.00003*X to provide a sufficiently strong magnetic field for accurate measurement and provide a sufficiently complex image to prevent counterfeiting. Preferably, 50,000*Y&gt;Z&gt;0.002 to provide for both magnetic measurements and image measurements. For example, magnetic particles having a combined volume of 0.01% of the mixture and non-magnetic particles having a combined volume of 0.02% of the mixture are effective in this application. Preferably, the ratio of the number of non-magnetic particles to the number of magnetic particles is between 1/10 and 2/1 inclusive, For example, magnetic particles with an average diameter of 200 microns and non-magnetic particles with an average diameter of 500 microns are effective in this application. 
         [0056]    The magnetizable particles may be flakes having an average thickness that is less than an average diameter of the flakes. Images of flakes vary with rotation of the flakes and provide additional complexity to the PUF. Preferably, the magnetizable particles have an average diameter of between 50 and 500 microns inclusive, and the non-magnetizable particles have an average diameter of between 200 and 2000 microns inclusive, to provide a sufficiently strong magnetic field for accurate measurement and provide a sufficiently complex image to prevent counterfeiting. Preferably, the non-magnetizable particles are much larger than the magnetizable particles e.g. the magnetizable particles have a first average diameter, the non-magnetizable particles have a second average diameter, and the second average diameter is at least twice as large as the first average diameter. This helps to reduce cost since smaller magnetic particles require less magnetic material and the larger non-magnetic particles are easier for an image sensor to measure. Preferably, the non-magnetizable particles are reflective to generate high contrast images and may include a low-cost metal such as aluminum. The magnetizable particles may contain neodymium and iron and boron. Alternatively, the magnetizable particles may contain samarium and cobalt. Preferably, the magnetic particles each have a diameter greater than 25 microns so they generate a sufficiently strong magnetic field to be detected with a low-cost detector. 
         [0057]    At block  1304 , the method causes the carrier to become solid. The carrier in be, for example, a liquid that is caused to become solid by adding a chemical, subjecting to ultraviolet light, increasing its temperature, etc. Alternatively, the carrier may be, for example, grains that are sintered. Causing the carrier to become solid locks the distribution and orientation of the particles. 
         [0058]    At block  1306 , the magnetizable particles are magnetized by, for example, subjecting the particles to a strong magnetic field. It is preferable to magnetize the particles to after the carrier is caused to become solid to prevent the particles from clumping together due to magnetic attraction. Alternatively, if suitable substrate materials are used that allow unformed aggregate pellets of the substrate material, magnetic particles and optical particles to be magnetized and later formed, the magnetic field orientation of the magnetic particles may be more random, and therefore more difficult to clone. Further, the application of a magnetizing field with patterned or randomized orientation may be applied to a formed substrate in order to cause greater diversity of magnetic field orientation. 
         [0059]      FIG. 14  shows an example embodiment of a method of making a security device according to one embodiment. Method  1400  makes an authentication device having a PUF and is thus difficult to counterfeit. 
         [0060]    At block  1402 , a non-volatile memory device is attached to a body. At block  1404 , a substrate is attached to the body, the substrate is configured to rotate about an axis and contains a plurality of magnetic particles. At block  1406 , first magnetic field data is generated by measuring along a first circular path centered on the first axis a first magnetic field generated by the magnetic particles. At block  1408 , second magnetic field data is generated by measuring along a second circular path centered on the first axis a second magnetic field generated by the magnetic particles, the second circular path encloses the first circular path. At block  1410 , first image data of the magnetic particles is generated as viewed along the first circular path. 
         [0061]    At block  1412 , the first magnetic field data, the second magnetic field data, and the first age data are encrypted. At block  1414 , the encrypted first magnetic field data, the encrypted second magnetic field data, and the encrypted first image data are written to the non-volatile memory device. Encryption prevents a counterfeit authentication device from fooling a PUF reader by presenting data measured from counterfeit particles stored in a non-volatile memory device. A counterfeit authentication device must correctly encrypt the data or the PUF reader will not be fooled. Encrypting data may include obscuring all the data, obscuring only some of the data, cryptographically signing the data, etc. 
         [0062]    Blocks need not be performed in the example order given. For example, blocks  1406 ,  1408 , and  1410  may occur before or after block  1402 . 
         [0063]      FIG. 15  shows an example embodiment of a method of making a security device according to one embodiment. Method  1500  makes an authentication device having a PUF and is thus difficult to counterfeit. 
         [0064]    At block  1502 , a non-volatile memory device is attached to a body. At block  1504 , a substrate is attached to the body, the substrate is configured to rotate about an axis, is non-opaque, and contains a plurality of particles. At block  1506 , first image data of the particles is generated as viewed from a first circular path centered on the axis illuminated using a first illumination line, the first image data corresponds to at least 360 degrees around the first circular path. At block  1508 , second image data of the particles is generated as viewed from the first circular path illuminated using a second illumination line, the second image data corresponds to at least 360 degrees around the second circular path. 
         [0065]    At block  1510 , encrypted image data is generated by encrypting the first image data and the second image data. At block  1512 , encrypted image data is written to the non-volatile memory device. As discussed above, encrypted data makes the authentication device more difficult to counterfeit. 
         [0066]    The foregoing description illustrates various aspects and examples of the present disclosure. It is not intended to be exhaustive. Rather, it is chosen to illustrate the principles of the present disclosure and its practical application to enable one of ordinary skill in the art to utilize the present disclosure, including its various modifications that naturally follow. All modifications and variations are contemplated within the scope of the present disclosure as determined by the appended claims. Relatively apparent modifications include combining one or more features of various embodiments with features of other embodiments.