The first three articles in this series reviewed contemporary security document serial number design strategies related to letterpress printing technology, security inks and font design. These three elements perform different security roles, in which the elements must complement and protect one another. Because font art may be the least developed of these concepts, yet is inexpensive to optimize, most future work in this series focuses on font design. This fourth article concerns numeral graphics that resist counterfeiter transposition between serial number positions. An additional benefit is an expanded numeral character set, which increases the quantity of unique graphics counterfeiters must manage.
Strategies in this article are for informational purposes only. Document issuers must decide which approaches, if any, are right for a particular document or compatible with manufacturing and/or quality control workflows. Specifically, Figures 3 through 21 just illustrate concepts that might be adapted for production fonts using different numeral shapes, a larger font size to accommodate more detail, fewer corners that might retain ink, strings including more than five positions, etc. Letterpress is assumed, but adaptation for novel digital serialization technology will be explored later in this series.
Novel numbering and character set
Part 3 of this series discussed novel numbering as a way to expand a numbering machine character set, which increases the pool of serial number graphics and modestly complicates counterfeiter transposition of serial number graphics captured from one position into other positions. Examples included Figure 1, in which proportional horizontal and vertical size scaling produce no font distortion, and Figure 2, in which taller characters are distorted versions of shorter characters. These examples provide a foundation for further work based on the template in Figure 3.
Figure 1. As described in Part 3 of this series, this is a full letterpress serial number at the left and height-normalized numerals from different locations in the string on the right. In this novel numbering string larger characters are scaled proportionally in both horizontal and vertical directions, so larger numerals are the same shape as smaller numerals. Compare to Figure 2.
Figure 2. As described in Part 3 of this series, this is a full letterpress serial number at the left and height-normalized numerals from different locations in the string on the right. In this novel numbering example numerals are scaled vertically but not horizontally, so taller numerals are stretched versions of shorter numerals, though each has approximately the same horizontal width. Compare to Figure 1.
In Figure 3, each row shows a serial number string (12345, 51234 or 45123) applied by a numbering machine. The gray rectangles are not part of the printed image but delineate the maximum image area on each relief surface. Vertical white boundaries represent the space between adjacent numbering machine wheels, such that numerals in each column originate from the same numbering machine wheel. In Figure 3 every wheel features an identical character set of just ten numerals (0-9), so for example, each “5” looks the same no matter where it appears. This means counterfeiters can capture a numeral graphic from any position (or redraw it) and transpose it to another position without editing or any visual cue that the transposition was done. Figures 4 through 21 explore serial number graphics designed to expose such transposition, and which are somewhat more complex to edit or redraw.
Figure 3. A mockup of the serial number design template used in Figures 4-21. Think of each row as a complete five-digit serial number applied from the same numbering machine but with a different sequence of numerals. This example has the same font on every wheel without clues that visually tie a numeral design to a specific position, so counterfeiter transposition of numeral graphics would be easy.
Position dependence and variables
The limitations of Figure 3 can be addressed by designing individual numeral graphics as part of a larger pattern that spans the entire serial number, and which associates each individual numeral graphic to one specific position on one specific wheel. In concept, this inhibits counterfeiters from capturing a numeral from one position in a genuine template document and transposing it to other positions to vary serial numbers across multiple counterfeits. In reality, counterfeiters can still assemble the complete library of numerals given multiple genuine template documents. This cannot be prevented absolutely but does make counterfeiting workflows more complicated and prone to error. Figures 1 and 2 featured font scaling but Figures 4 through 13 illustrate rotation (Figures 4-5), distortion (Figures 6-7), external art (Figures 8-9), contour line placement (Figures 10-11) and contour line thickness (Figures 12-13).
Figure 4. A mockup like Figure 3, except that position-dependent rotation has been applied. Numerals in the first position are always rotated counterclockwise and those in the last position are rotated clockwise, regardless of the numeral. Similarly, each of the middle positions has its own unique degree of rotation, so each wheel has its own distinct character set. Compare to Figure 5.
Figure 5. Counterfeiter transpositions of the same numerals as in Figure 4 to generate different serial numbers for each of multiple counterfeits. Disruption of the pattern shows which numerals were moved. Rotation only alters the position of a numeral but not its shape, so a counterfeiter could simply rotate numeral graphics as needed to better fit them into various positions. Compare to Figure 4.
To begin, Figure 4 shows the same serial numbers as Figure 3 but rotated. No matter which numeral, each wheel always features a specific degree of rotation. Figure 5 contains the same graphics as Figure 4, except that two numerals are transposed in each row, as a counterfeiter might do when shuffling captured numeral graphics to vary serial numbers between multiple counterfeits. Figure 5 provides a visual cue that transposition has occurred, since the rotation pattern is disrupted. However, this strategy presents only a minor problem for counterfeiters since the total character set is still just ten numerals, which counterfeiters can capture and rotate without major editing or redrawing or graphics.
A limitation of both Figures 3 and 4 is that numeral shapes are identical across all numbering machine wheels. In Figure 6 each wheel position features its own unique distortion, so in Figure 6 the total numeral set is 5 X 10 = 50 distinct numeral shapes, as opposed to just ten in Figure 4. This simple distortion is only somewhat more complex than just rotation and could be reverse engineered relatively easily. Figure 7 contains the same graphics as in Figure 6 except transposed by a counterfeiter, with visible disruption to the pattern. Figure 6 might be improved if the font was both distorted and rotated, and the appearance of the final design could be dependent on which operation was done first.
Figure 6. A mockup like Figure 4, except that position-dependent warp has been applied. As in Figure 4, every position has its own unique character set. Unlike in Figure 4, the shape of each numeral is modified and not just its orientation. However, these numerals are just derivatives of the same font, and the nature of the warp can easily be identified because it’s simple. Compare to Figure 7.
Figure 7. Counterfeiter transpositions of the same numerals as in Figure 6 to generate different serial numbers for each of multiple counterfeits. Just as in Figure 5, transposition of characters without edits makes it easy to see which ones are out of order, but counterfeiters can still reverse the warp to fit numeral graphics into new positions. Compare to Figure 6.
Adding external graphics is another way to create a continuous visual pattern. Figure 8 shows identical numerals to those in Figure 3, but with two curved lines spanning the sequence. Figure 9 shows the characters in Figure 8 transposed by a counterfeiter, with certain numerals standing out because line continuity is disrupted. Since the font itself is not different between positions, counterfeiters need only edit or redraw the lines to prepare graphics for transposition. The strategy in Figure 8 could be improved if the font itself was also unique to each position (as in Figure 6).
Figure 8. Another mockup like Figures 4 and 6, except that the numeral graphics themselves are the same across positions while waves have been added around the numerals. As with the previous examples, each wheel has its own character set and a counterfeiter seeking to transpose a numeral between locations would edit the wave design rather than the numeral font. Compare to Figure 9.
Figure 9. Counterfeiter transpositions of the same numerals as in Figure 8 to generate different serial numbers for each of multiple counterfeits. Just as in Figures 5 and 7, transposition of characters without edits to the wave design makes it easy to see which ones are out of order, but counterfeiters could edit the wave design to accommodate numerals to new positions. Compare to Figure 8.
Hollow numeral artwork allows for contour lines based on thickness as in Figure 10 or placement as in Figure 12, with respective transpositions by a counterfeiter in Figures 11 and 13. The line thickness differences in Figures 10 and 12 are less amenable to simple editing than previous examples and might encourage counterfeiters to risk errors in redrawing graphics from scratch. Quality control concerns about letterpress ink buildup in the enclosures might be mitigated with a more forgiving font design, use of a ribbon consumable instead of an ink, application of an ink-repelling coating over non-image areas of the relief plate surface, or other means.
Figure 10. A serial number design based on hollow numerals and increasing thickness of a contour outline. Because the line thickness is an integral part of the numeral design and not an edit that can be easily reversed, this approach may encourage redrawing errors. As with prior examples, moving numeral graphics between positions creates a visual cue that numerals are out of order.
Figure 11. Counterfeiter transpositions of the same numerals as in Figure 10 to generate different serial numbers for each of multiple counterfeits. In Figures 5, 7 and 9, counterfeiters could reverse rotation and warp, or make relatively simple edits to a wave design. In this example, editing captured graphics may be harder than redrawing a graphic entirely. Compare to Figure 10.
Figure 12. A serial number design based on an outline as in Figure 10, but with line thickness changing with position. The first numeral shows a thicker line at the upper left and the last a thicker line at the lower right, etc. Line thickness is part of the numeral design and not something that a counterfeiter can easily edit, so this approach may encourage redrawing and provide more chance of error.
Figure 13. Counterfeiter transpositions of the same numerals as in Figure 12 to generate different serial numbers for each of multiple counterfeits. Just as with Figure 10, in this example editing captured graphics may be harder than redrawing the graphic from scratch, and the process of redrawing a graphic entirely increases the chance of counterfeiter error. Compare to Figure 12.
Integrating multiple variables
The single-variable examples in Figures 4 through 13 are not complex enough to inhibit counterfeiter reverse engineering or transposition in real document applications. Better results can be obtained by using multiple variables together, as is demonstrated in Figures 14 through 16.
Figure 14 includes three variables: font size, contour line thickness and baseline position. As the font size grows larger from left to right, the contour line thins. This is intentional because if a counterfeiter enlarges a scanned numeral from the first position to fit the last position, it will exaggerate the contour line, making it too thick where it should be the thinnest. Similarly, if a numeral from the last position were scaled down to the first position size, its contour line would barely be visible. Of the variables in Figure 14 the placement of the numeral relative to the baseline may be the least significant because, like the rotation in Figure 4, it’s just a repositioning and not an artwork change.
Figure 14. A serial number simultaneously incorporating three visual cues: size, contour line thickness and baseline position. From left to right size increases but line thickness decreases. This relationship is deliberate; enlarging a small numeral from the first position would increase line thickness too much. Similarly, shrinking a larger numeral would similarly make the contour line too thin.
Figure 15. Expansion of the mockup in Figure 14 to add a baseline to the artwork. As shown in Figures 4 through 13, repositioning graphics is simpler for counterfeiters than changing images. The printed baseline in this example forces additional edits to transposed images instead of just repositioning, and also makes numeral placement relative to the baseline easier to see. Compare to Figure 14.
One way to improve Figure 14 is emphasizing the baseline. In Figure 14 the baseline placement is subtle, but in Figure 15 the baseline is part of the art. Attempting to enlarge or shrink a complete numeral graphic in Figure 15 for counterfeiting will also enlarge or shrink the baseline, prompting counterfeiters to redraw rather than resize the baseline graphic. Essentially, this converts the baseline from a purely positional characteristic to part of the image that requires editing or redrawing to transpose.
Figure 16. Expansion of the mockup in Figure 14 to include a wave. The design variables now include not just size, contour line thickness and baseline position, but also wave shape, placement, thickness, and position. The addition of the wave makes more complete use of the relief plate surface, adds a strong visual cue, and provides more opportunity for counterfeiter error. Compare to Figure 15.
Figure 17. Counterfeiter transpositions of the same numerals as in Figure 16 to generate different serial numbers for each of multiple counterfeits. Compared to prior examples of transpositions featuring only one design variable, here multiple visual cues make transposed numerals stand out. There are no simple edits that allow counterfeiters to quickly fit numerals into new positions. Compare to Figure 16.
Continuing to improve on Figures 14 and 15, the wave in Figure 16 provides yet another visual check against numeral transposition. Figure 16 already incorporates size, contour line thickness, baseline position and baseline artwork, but more variables could be added, especially considering the font itself remains unmodified. Transpositions of Figure 16 for counterfeiting are shown in Figure 17. In comparing the multivariable example in Figure 17 to single variable examples in Figures 5, 7, 9, 11 and 13, the transpositions in Figure 17 are easier to see. Additionally, consider the relative difficulty of editing a numeral in Figure 16 as compared to a numeral in, for example, Figure 8. Again, the goal of designing letterpress serial numbers that counterfeiters cannot redraw is purely aspirational, but more complex designs still add labor, complicate counterfeiting workflows, and provide opportunity for error.
To further illustrate the range of possible design approaches, Figures 18 and 19 present a second multivariable example that incorporates baseline adjustment, rotation, a partial contour line, and a curved wave joined to the contour line to convert the rotation into part of the art instead of just a repositioning. Like Figure 16, Figure 18 does not include any position-dependent distortion of the actual font graphics, so adding some would be a simple way to improve it.
Figure 18. An alternate multivariable strategy implementing rotation, contour line placement/width, baseline position and a wave. This explores the scope of possibilities within serial number variables since this design includes some of the same strategies as Figure 16 but looks very different than Figure 16. The actual numeral font hasn’t yet been modified but could be. Compare to Figure 16.
Figure 19. Counterfeiter transpositions of the same numerals as in Figure 18 to generate different serial numbers for each of multiple counterfeits. Just as in Figure 17, the incorporation of multiple design variables makes out-of-place numerals easier to see in this example than in many of the prior Figures featuring transpositions. Compare to Figure 18.
Considerations and context
Figures 4 through 19 devoted significant attention to font designs that 1) provide visual cues when numerals are transposed; 2) cannot be easily repositioned or edited for transposition; 3) require some work to redraw to increase opportunities for counterfeiter error; and/or 4) maximize the character set by using a custom numeral graphic on every relief surface on every wheel in the numbering machine. Besides these font design concepts some related topics have not yet been addressed.
For example, Figures 4 through 19 are explained in the context of manual font design, but algorithmic font development could offer new potential for position dependent patterns. Similarly, relief plate surface artwork as introduced in Part 1 of this series was not explored here in the context of position dependence, though it will be later in this series, as will font design for digital serialization methods. Further, the numbering machine wheels were assumed to be of the same width and with the same quantity of relief surfaces. Wheels of varying width were not considered, nor were wheels potentially containing more than ten relief surfaces. Varying serial number designs for multiple document types was also not considered. For example, use of a subtly (or even overtly) different serial number font for each banknote denomination in a series, various passport types from the same issuer, or similar series/version designations in other security document types could help expose transposition not just between positions in one document, but also between document types, versions or variations.
Detection criteria and methods are also an important consideration. Though the main theme of Figures 4 through 19 is visual detection of transposed characters, counterfeiter errors in editing or redrawing serial number graphics could also provide a means of detection. Questions include not just whether or how a human could identify such artwork errors and whether prior knowledge of the true font design would be needed to do so, but also whether imperfect counterfeiter simulations of complex serial number art could be identified from camera images in a machine inspection system like a banknote sorting machine, passport reader, or even a smartphone camera.
Figure 20. Serial numeral mockups in which every printing surface on every wheel in the numbering machine features a customized unique numeral graphic based on a standard base font. This increases the total character set in the numbering machine, but unlike the examples in Figures 4-19, there is no human-recognizable visual pattern that spans across the entire string. Compare to Figure 21.
Figure 21. Counterfeiter transpositions of the same numerals in Figure 20, which do not disrupt a visual pattern because there is no pattern to disrupt. However, machine readers could automatically identify out-of-place graphics whether or not a larger pattern is present. This type of numeral customization could be combined with larger pattern strategies to capture advantages of both. Compare to Figure 20.
For example, Figure 20 shows three serial numbers in which the numeral designs are position dependent, but in a way that does not produce a visual pattern than spans the entire serial number. Figure 21 shows the transposition of graphics from Figure 20. At a glance, it would be hard for a human to detect transpositions in Figure 21 because there is no pattern disruption. Given a reference showing all of the graphics on each wheel, a human could manually analyze each graphic to determine whether each numeral was of the correct design and in the correct position, though this would be slow. However, the arbitrary nature of the customizations in Figure 20 could be a good fit for machine inspection because machines do not require a visual pattern to determine if any numeral graphic is out of place. Additionally, such quasi-random graphics make it hard for counterfeiters to extrapolate unknown numeral designs. This is relevant when a counterfeiter only has access to a single genuine pattern document containing just a small subset of the serial number graphics used in that document type and redraws missing serial number graphics without knowing exactly how those graphics should look.
Conclusion
The design concepts illustrated in this article can be low in cost, increase counterfeiter labor, provide more chances for counterfeiters to make errors editing or redrawing, and expose transposition between positions. But numeral graphics are limited in size and graphical complexity, so counterfeiters can replicate even a significantly expanded character set given time and a collection of genuine template documents. This underscores why maximizing serial number security requires serial number art to work in concert with the printing and ink strategies described in the first two parts of this series. Yet it is also possible to develop serial numbers in which the quantity of numeral graphics printable from a given numbering machine exceeds the quantity of relief surfaces available on that numbering machine. This additional expansion of the character set requires numeral graphics be constructed from more than one letterpress impression, which will be explored Part 5 of this series.
Disclaimer: This document represents the opinions of its authors and not necessarily the opinions of the U.S. government. The technologies and strategies described may not be available, appropriate, or manufacturable for all document issuers. The examples shown do not imply anything about the quality of a document, its designer, its manufacturer, or the issuing authority. For informational purposes only.
Joel Zlotnick is employed by the US Department of State, Bureau of Consular Affairs, Counterfeit Deterrence Laboratory as a physical scientist. His current work involves research in security artwork and design techniques in security printing. He is an instructor on counterfeit detection at the US Department of State Foreign Service Institute.
Tyra McConnell is a Forensic Document Examiner at the US Department of State, Bureau of Consular Affairs, Counterfeit Deterrence Laboratory. She provides training on security documents and develops presentations and e-learning courses regarding counterfeit detection.
