This series about serial number optimization has covered letterpress, ink properties, font design, and position dependence. Two deficiencies of the position dependence concepts as described in the fourth article in this series are that the character set is still too small, and there is no potential for an algorithmic means of deriving or selecting serial numeral graphics based on serial number data. In this fifth article, serial numerals printed in multiple steps are proposed as a solution. Here, some of the wheel graphics in a letterpress numbering machine are partial characters. When two partial numeral graphics are overprinted to create what will now be termed a legible “composite numeral,” a serial number character set larger than the number of relief surfaces in the numbering machine becomes possible.
The strategies discussed in this paper are for informational purposes only. Document manufacturers and issuers must decide which, if any, are appropriate for a particular security document or are compatible with manufacturing and/or quality control workflows. Figures 1-14 only illustrate concepts that might be better executed using technically different or more attractive artwork, a larger font size than is typical for security document serial numbers, bolder differentiation between the details of similar characters, a font design that is more forgiving of registration variations, etc.
Review: Position dependence and character set
The mockup graphics in Figure 1 were introduced in Part 4 of this series and illustrate three position dependent serial numbers that could be applied by a theoretical numbering machine containing five wheels. Since letterpress numbering machines contain a limited number of wheels and each wheel contains a limited number of relief printing surfaces, there are mechanical constraints on the quantity of graphics. If each wheel has ten relief surfaces (0-9), the total character set in Figure 1 is limited to 5 * 10 = 50 visually distinct numerals. This is more than conventional numbering machines that repeat the same ten graphics on every wheel, but just 50 characters leaves room for improvement.
Figure 1. From Part 4 of this series, three mockup serial numbers with position dependent graphics. Each row represents one possible serial number from one numbering machine. Unlike conventional numbering machines that use the same character set on all wheels, this font relates numeral design to numeral position. The light gray background shows the maximum image area on each relief surface.
While Part 4 emphasized preventing counterfeiter transposition of graphics and the size of the character set was secondary, now the main priority is expanding the quantity of numeral designs. One way to overcome the mechanical limitations inherent in letterpress numbering machines is to design the true wheel graphics as partial shapes and construct legible numerals by overprinting two or more impressions on a programmable numbering machine. An example is described in the next section.
Composite numerals
Composite numeral wheel graphics cannot be designed like typical fonts because they must both 1) allow every numeral from 0-9 to be created in at least one way and 2) increase the quantity and complexity of numerals in the full character set as much as possible. Balancing these priorities is a big topic that cannot be explored fully here, so just one representative example is illustrated in Figure 2.
Figure 2. A nonstandard character set in which the characters may or may not be complete numerals. The ten positions on the numbering wheel are therefore not designated by a numeral, but instead positions are referenced alphabetically from A through J. These characters are applied in an opaque black ink that obscures underlying art or a prior letterpress impression.
Figure 2 shows a mockup of graphics applied by each of ten relief surfaces in a single numbering machine wheel. This is the true font. Each position is identified by a letter (A-J) because five of the graphics are not numerals. Composite numerals contain two impressions, so except for double printing of shapes A through E, the graphics in Figure 2 do not appear in isolation in issued documents.
Figure 3 illustrates how the wheel graphics in Figure 2 can be overprinted to create the numeral “9” in four ways, if registration is good. Each “9” can be differentiated from the others by subtle variations in shape and line thickness, but because this example includes opaque black ink, areas that contain two overlapping ink layers are obscured.
Figure 3. Four examples of how the legible numeral “9” can be produced by two sequential impressions of the character set in Figure 2, without accounting for print order. A different font design might allow for more or fewer ways of creating “9” or other numerals. In opaque black ink, the shape of each “9” is slightly different but which areas contain two overlapping ink layers is not obvious.
Extrapolating to the whole character set, Figure 4 shows how the ten wheel graphics in Figure 2 can be overprinted to form 29 composite numerals. This quantity is particular to the specific Figure 2 font, and a different set of wheel graphic designs could produce more or less than 29 combinations and/or a different distribution of options among the numerals.
Figure 4. The full set of 29 legible numerals that can be assembled by overlapping two of the numbering wheel graphics shown in Figure 2. Each numeral is recognizable, but also graphically different from other designs of the same numeral. Because the ink is opaque black, these examples are differentiated by contour shape and not by visibility of the ink layers.
Options for enhancement of the template in Figures 2 through 4 could include translucent ink to ease inspection by showing ink layers, algorithmic composite numeral selection that functions like a graphical check digit, revisiting position dependence to impede counterfeiter transposition of graphics, etc.
Opacity and ink layer visibility
Ink translucency was discussed in Part 2 of this series and is revisited in context here. Figures 5 through 7 feature the same mockup graphics in Figures 2 through 4, except in translucent ink. Contour shape is the main difference between the opaque composite numerals in Figure 4, but the translucent examples in Figure 7 differ by both contour shape and by which parts of the graphic show one or two ink layers.
Figure 5. The same nonstandard character set as in Figure 2, except that the blue color indicates that these impressions are applied in translucent blue ink instead of opaque black. Ink opacity will become relevant as two (or more) letterpress impressions are applied to form legible numerals in later figures, many of which include overlapping letterpress print. Compare to Figure 2.
Figure 6. The same combinations of two characters shown in Figure 3, except applied in translucent blue ink instead of opaque black. Parts of the image where two ink layers overlap are visibly different from areas containing only one layer of ink. This visual cue shows differences between composite numerals more clearly, as opposed to reliance mainly on contour shape as in Figure 3.
Figure 7. The same set of 29 legible numerals shown in Figure 4, except in translucent blue ink instead of opaque black. Like Figure 4 these numeral graphics can be differentiated by contour shape, but the translucent ink also highlights which parts of each numeral include two layers of ink or just one layer of ink. Compare to Figure 4.
Showing the ink layers as in Figure 7 allows easier verification that each composite numeral does include two distinct wheel graphics, and that each is of the correct design. The former could help reveal counterfeit serial numbers that are simulated in only one printing step, and the latter matters if an algorithm determines when or how a particular composite numeral is selected over other choices.
Algorithmic composite numeral selection
Figures 4 and 7 show options but do not indicate how the serialization system decides, for example, which “9” should be selected out of the four choices. This can be done randomly or algorithmically. Given a numbering machine in which all five wheels contain the graphics in Figure 2, Figure 8 shows three example serial numbers in which composite numeral designs were selected randomly. Figure 9 shows the same characters but in translucent ink. Both Figures 8 and 9 show no apparent link between the design of a composite numeral to either its placement in the string or the serial number data.
Figure 8. Three possible serial numbers drawn from the numeral set in Figure 4. How composite numerals are selected may be determined randomly or algorithmically. Here, numerals in all positions were randomly selected from the character set in Figure 2. However, in real documents each position should have a custom set like but not identical to the set in Figure 2. Compare to Figure 4.
Figure 9. The same serial numbers shown in Figure 8 but printed in translucent blue ink and drawn from the combinations in Figure 7. Like Figure 8 these graphics can be differentiated by shape, but unlike Figure 8, the ink layers can also be seen and contribute to each character’s visual distinctiveness. A better way would be for each wheel position to have its own character set. Compare to Figures 7 and 8.
But in a programmable numbering machine, numeral selection could be algorithmic. Suppose which composite numeral design is chosen depends on the following: its position in the string, whether the preceding numeral is even or odd, whether the value of the following numeral is “3” or higher, a mathematical calculation based on serial numeral data, the selection of other composite numerals in adjacent positions, or other criteria. Simply, this is a graphical check digit system in which composite numeral designs are selected based on and can be verified using serial number data. The goal is not absolute cryptographic security, but just to provide a new opportunity for counterfeiter error.
A simple algorithm, such as only one specific composite numeral design allowed in a specific position, could be confirmed visually but adds limited security. More complex visual and mathematical derivations of numeral graphics would be hard to confirm manually, but a machine reader or smartphone camera could validate the right combinations of graphics throughout a full serial number. Either way, for lay users the macro serial number data could still be read normally.
A limitation of Figures 8 and 9 is that the 29 designs in Figures 4 or 7 comprise the entire character set, since every wheel has the same graphics. Further character set expansion may be achieved by position dependence, character level customizations and/or print order. Each is discussed below.
Position dependence revisited
Some of the position dependence concepts introduced in Part 4 of this series can be adapted for composite numerals. Figures 10 and 11 show three serial numbers based on the 29 graphics in Figures 4 and 7, but with distortion that differs between wheels yet is the same for all positions on one wheel. These techniques are complementary because the composite numerals expand the character set and the distortion complicates counterfeiting workflows, especially counterfeiter transposition of graphics.
Figure 10. Three serial numbers drawn from the character set in Figure 4, but with a simple position dependent warp applied differently to each wheel. This warp example, while not complex enough for real document applications, generally illustrates how position dependent graphics “lock” each composite numeral to a specific location, inhibiting transposition of graphics by counterfeiters.
Figure 11. The same three serial numbers in Figure 10 with the global warp applied but printed in translucent blue ink so areas containing two layers of ink become visible. Each numeral is made unique not only by its shape and the locations where two layers of ink overlap, but also how each numeral is affected by the warp depending on its position within the string. Compare to Figure 10.
Because each of the five wheels in Figures 10 and 11 contains a modified version of the composite numerals in Figures 4 and 7, the numbering machine supplies a total of 5 * 29 = 145 unique composite numerals. Without composite numerals a wheel with ten positions can only supply ten graphics, which is why Figure 1 and other examples in Part 4 of this series were limited to 50 graphics on five wheels.
Character-level customizations revisited
Also, from Part 4 of this series, another option for character set expansion is customizing each wheel graphic with breaks, serifs, line thicknesses, etc. The first column of Figure 12 shows the exact C and E graphics from Figure 2, with modified versions of the original C and E graphics in the second through fifth columns and as they would appear printed from the second through fifth wheels. The bottom row of Figure 12 shows how the C and E graphics combine for each position.
Figure 12. Some graphically altered versions of “C” (top row) and “E” (middle row) from Figure 2 to form new “C + E” (bottom row) combinations as in Figure 4. The first column shows the exact characters from Figure 4. The second through fifth columns show variations in line thickness, line breaks, serifs, etc. such that each wheel has its own custom character set. Compare to Figures 2 and 4.
Figure 13. The same position-dependent “C + E = CE” combinations shown in Figure 12 but printed in translucent blue ink, so the ink layers become visible. The “C + E” combinations in the bottom row can still be differentiated by shape as they can in Figure 12, but here the ink layers are visible and make the differences between similar numerals easier to see. Compare to Figure 12.
Because in Figure 12 the ink is opaque, the C + E composite numerals in the bottom row mask the locations of breaks where the two impressions overlap. In contrast, the same composite numerals applied in translucent ink in Figure 13 are easier to differentiate because they show ink layer placement.
Both position dependence (Figures 10 and 11) and character customization (Figures 12 and 13) contribute to an expanded character set, though Figures 12 and 13 do not provide a visual signal relating design to placement. Which approach is best may depend on whether the serial number is primarily inspected by humans or machines, or both approaches can be integrated together.
Print order and the letterpress halo
Part 1 of this series described a “halo” of ink as one of the most distinctive characteristics of letterpress printing. If two letterpress images are superimposed, the halo from the first impression could be flattened where it is impacted by the second impression. If so, microscopic halo placement in a composite serial number depends on print order, as illustrated in Figure 14.
Figure 14. A model of how the print order of two letterpress impressions might affect halo visibility, shown by shapes from Figure 5. The dark contour lines indicate halo placement. If A is applied over J, the (still wet) halo of J could be flattened where impacted by A, and the reverse if J is applied over A. If true, then “A over J” and “J over A” could be considered different characters on a microscopic level.
If halo placement is controlled by print order and microscopic human or machine inspection of the halo is practical at least in some circumstances, then the quantity of characters in Figures 4 and 7 nearly doubles to 29 + 24 = 53. The reason the total is not 29 + 29 = 58 is that AA, BB, CC, DD and EE are just the same graphics applied twice. Combined with position dependence and/or character customization strategies that make each wheel unique, optimizing and extrapolating the Figure 2 character set across five wheels could further enlarge the character set to a total of 5 * 53 = 265 composite numerals.
Considerations and context
Composite numerals (Figure 2-9), position dependence (Figures 10-11), character customizations (Figures 12-13) and print order (Figure 14) could be used simultaneously, but there are still more variables. Consider how design of a font like in Figure 2 would change if each wheel had more than 10 relief surfaces, or if each composite numeral combined three (or more) impressions instead of two.
Also consider how composite numeral strategies could be integrated with concepts from earlier parts of this series. For example, adding textured artwork to numbering machine relief surfaces (Part 1 of this series) could supplement contour shape, ink layers and halo placement as another way of differentiating between otherwise identical composite numeral designs. For example, two composite numerals could feature the same macro artwork but different microscopic surface textures, with the version selected algorithmically. Another example might be whether the UV response of a serial number ink (Part 2 of this series) might brighten where applied in two layers, and if so, how that benefits inspection.
Composite numerals have so far been treated as a way to differentiate wheels within one numbering machine, but the concept could be extended across multiple document types. If each denomination in a banknote series or each plate position in a banknote sheet featured composite numerals with microscopic customizations but the same general macroscopic appearance, counterfeiters substituting graphics between denominations would risk detection. Similarly, different versions of travel or identity documents (i.e. regular, emergency, and diplomatic passports) could also be customized.
Conclusion
Options in this paper support more character set expansion than in Part 4 of this series while also revisiting position dependence and introduce algorithmic selection of composite numeral designs. This can make serial number counterfeiting not just about scanning and transposition of graphics, but also about correctly identifying and simulating the correct composite numeral constructions for each specific position within a specific serial number sequence. Customization of composite numeral designs by contour shape or ink layers as described above might best be described as an enhanced second level (covert) security feature. If multicolor composite numerals could also be differentiated by color placement, the inspection level shifts towards first level (overt), potentially expanding serial number utility for both human and machine inspection. This series will next introduce serial numbers featuring two ink colors, applied by two different numbering machines in two different fonts.
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.
Sources/References:
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.
