  Biometry has proved its capability in terms of recognition accuracy. Now, it
is widely used for automated border control with the biometric passport, to
unlock a smartphone or a computer with a fingerprint or a face recognition
algorithm. While identity verification is widely democratized, pure
identification with no additional clues is still a work in progress. The
identification difficulty depends on the population size, as the larger the
group is, the larger the confusion risk. For collision prevention, biometric
traits must be sufficiently distinguishable to scale to considerable groups,
and algorithms should be able to capture their differences accurately.
  Most biometric works are purely experimental, and it is impossible to
extrapolate the results to a smaller or a larger group. In this work, we
propose a theoretical analysis of the distinguishability problem, which governs
the error rates of biometric systems. We demonstrate simple relationships
between the population size and the number of independent bits necessary to
prevent collision in the presence of noise. This work provides the lowest lower
bound for memory requirements. The results are very encouraging, as the
biometry of the whole Earth population can fit in a regular disk, leaving some
space for noise and redundancy.
