Counterfeit Deterrent Features for the Next-Generation Currency Design (1993)

The random pattern/encryption concept as applied to currency uses random three-dimensional patterns as positive identifiers to distinguish authentic from counterfeit notes. The concept was originally developed to provide positive identification of specific items for intelligence and arms control applications; that us, once a particular missile was inspected and identified as missile that was allowed by the treaty, it was necessary to ensure that the exact same missile was the one found in a later inspection (Graybeal and McFate, 1989). This concept can be extended to provide a high degree of counterfeit deterrence for banknotes.

The identifier must initially be read and a description of it created that is stored for future reference. To authenticate the positive identifier, the same random pattern is read again and compared with the recorded description. If they match, authentication occurs.

In practice, initial and subsequent readings of an identifier will differ because of unavoidable variations in the location of the reader with respect to the pattern, variations in the sensors, resolution limits of the sensors, and changes in the pattern resulting from wear and tear. These differences could cause false decisions by judging that the patterns are the same when actually they are different (a false positive) or judging that the patterns are different when actually they are the same (false negative).

A number of methods have been developed and tested that take these errors into account and ensure very low probabilities of false decisions. These methods take advantage of the fact that it is not necessary for authentication purposes to exactly match the true pattern with that read subsequently. It is only necessary to distinguish between the distribution of correlation numbers of like patterns and the distribution of the correlation numbers of unlike patterns. If a large number of readings are taken of the same pattern and correlated with each other, random reading errors will cause variations in the correlation numbers. If the correlation numbers are plotted, they will approximate a normal distribution. The peak value and the standard deviation (spread) of the values will depend on the sources of error. Similarly, when a large number of unlike patterns are read and correlated, they will generate a different distribution with a peak at a lower value. If there is a complete separation between these curves, a threshold correlation value between the peaks can be selected such that all correlation numbers below that value result from correlation of unlike pattern descriptions and all correlation values above the threshold number result from correlation of like pattern descriptions. In the ideal case, there would never be a false decision. In practice, there will

rarely be complete separation between the curves. Also, it is theoretically possible that two randomly generated patterns, regardless of how complex they are, will be exactly the same. For complex patterns, this probability is infinestimally small.

The reading errors mentioned above increase the overlap between the curves. The result is that there is a chance of making a false decision. This has been the subject of considerable research and development, which has identified methods that account for these errors and ensure an acceptable probability false decision. In the application for arms control verification mentioned above, substantial effort was devoted to adversary analysis to ensure that the random patterns could not be counterfeited successfully and that both the false negatives and false positives resulting from correlations of pattern readings taken in the field would be less than one in a million.

A simple method for minimizing concerns regarding misalignment of the reader with the pattern on successive readings is to desensitize the spacial resolution of the pattern reading. This is done by placing the locations of the features that are read into bins (or cells) that are larger than the alignment errors. While this reduces the effective number of pattern features that are used for identification, with certain patterns there is still enough random information to result in acceptable false-decision probabilities if the alignment errors are not very large. This method proved to be successful in the proof-of-concept demonstration of the random pattern/encryption concept that was conducted for the Bureau of Engraving and Printing, and which used fiber-optic patterns (Kromer, 1987).

Various concepts were developed and tested that eliminate errors caused by variations in the alignment of the reader for certain patterns. The complex pattern reading is transformed into a series of coefficients. This results in a description of the pattern with respect to itself instead of with respect to an external reference frame. If the patterns are completely covered by the reader and no information outside of the pattern is read, the descriptions of the readings are the same regardless of the position of the reader. Comparison of the transform coefficients allows authentication of the pattern descriptions (Ahmed et al., 1986).

Another method developed to reduce the sensitivity to reading errors employs a computer program to shift the patterns with respect to each other and correlate them at each relative orientation. The maximum correlation-value occurs when the two patterns are registered correctly. This value is used for comparison with the threshold decision correlation value to indicate whether or not the pattern descriptions represent the same pattern.

A variation of this method shifts and correlates small areas of the patterns (instead of shifting the entire pattern on a trial and error basis) until a peak value is found for each area. This approach reduces the amount of computer manipulation of images and reduces the time required to determine the correct alignment of the pattern descriptions. The distance and direction that each area was shifted to get a peak correlation number is used to calculate how to shift the whole pattern with respect to the other pattern, both in translation and in rotation, to register them accurately. Then the complete patterns are correlated (Tolk, 1992).

Another approach compensates for errors in the reader location with respect to the pattern. It results in low false-decision probabilities even if a large portion of the unique identifier is missing because of wear and tear. This can be illustrated by two images made from a photograph of a unique identifier. The significant features of the pattern appear as transparent spots. The rest of the area is made opaque. The images are then overlaid. Consider

n locations on the transparency, with each location having probability p of being transparent. Then the expected number of transparent locations when the two transparencies are registered with each other is N_R=np

If the images are not registered with each other, the expected number of transparent locations is N_NR=np²

Thus, the expected ratio R of matching transparencies in the registered position to the matching transparencies in the unregistered position is

If damage to the pattern causes a loss of transparencies equal to k times the original number of transparencies, the expected number of matching patterns in the registered position of the patterns is N_R=n (p−kp)

The expected number of matching transparencies in the unregistered position is N_NR=n (p−kp) p

The expected ratio of matching transparencies in the registered position to the matching transparencies in the unregistered position then is

This result for the damaged pattern is the same ratio as that for the undamaged pattern. Thus, wear and tear of a pattern does not change the expected value of this ratio, although it does change the variance. If different random patterns that possess the same proportion of transparencies to opacities are overlaid, the expected number of matching transparencies is np² regardless of the registration. The criteria for deciding whether or not two readings are from the same pattern is based on the ratio of transparencies in the registered and unregistered orientations exceeding a chosen value (Bauder, 1983).

Ahmed, N., R. Kruker, and D. Park. 1986. Authentication Scheme for Random Patterns Using Transforms. University of New Mexico memo to Don Bauder, Sandia National Laboratories. August.

Bauder, D. W. 1983. An Anti-Counterfeiting Concept for Currency. Systems Research Report PTK-11990. Albuquerque, N.M.: Sandia National Laboratories.

Graybeal, S. N., and P. B. McFate. 1989. Getting Out of the STARTing block. Scientific American261(6)64–65.

Kromer, R. P. 1987. Demonstration of a Random Label Counterfeit Deterrence System (RLCDS) for Currency. Sandia National Laboratories. May 1, 1987. Unpublished.

Tolk, K. 1992. Reflective particle technology for identification of critical components . Institute of Nuclear Management, 33rd Annual Meeting Proceedings, July, 1992. Vol. 21pp.xxi., Northbrook, Ill.: American Materials Proceedings.