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The accuracy of biometric identification depends on the chance of a false positive: the probability that the identifiers of two persons will match. Individuals whose identifiers match might be termed duplicands. When very many people are to be identified success can be measured by the (low) proportion of duplicands. The Government of India is engaged upon biometrically identifying the entire population of India. An experiment performed at an early stage of the programme has allowed us to estimate the chance of a false positive: and from that to estimate the proportion of duplicands. For the current population of 1.2 billion the expected proportion of duplicands is 1/121, a ratio which is far too high.

The article was published in Economic & Political Weekly, Journal » Vol. 51, Issue No. 9, 27 Feb, 2016.

A legal challenge is being mounted in the Supreme Court, currently, to the programme of biometric identification that the Unique Identification Authority of India (UIDAI) is engaged upon: an identification preliminary and a requisite to providing citizens with “Aadhaar numbers” that can serve them as “unique identifiers” in their transactions with the state. What follows will recount an assessment of their chances of success. We shall be using data that was available to the UIDAI and shall employ only elementary ways of calculation. It should be recorded immediately that an earlier technical paper by the author (Mathews 2013) has been of some use to the plaintiffs, and reference will be made to that in due course.

The Aadhaar numbers themselves may or may not derive, in some way, from the biometrics in question; the question is not material here. For our purposes a biometric is a numerical representation of some organic feature: like the iris or the retina, for instance, or the inside of a finger, or the hand taken whole even. We shall consider them in some more detail later. The UIDAI is using fingerprints and iris images to generate a combination of biometrics for each individual. This paper bears on the accuracy of the composite biometric identifier. How well those composites will distinguish between individuals can be assessed, actually, using the results of an experiment conducted by the UIDAI itself in the very early stages of its operation; and our contention is that, from those results themselves, the UIDAI should have been able to estimate how many individuals would have their biometric identifiers matching those of some other person, under the best of circumstances even, when any good part of population has been identified.

Read the full article here.

The author thanks Nico Temme of the Centrum Wiskunde & Informatica in The Netherlands for the bounds he derived on the chance of a false positive. He is particularly grateful to the anonymous referee of this journal who, through two rounds of comment, has very much improved the presentation of the results. A technical supplement to this paper is placed on the EPW website along with this paper.

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