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Number of biometric samples required to form an exhaustive set of fingerprint hashes?

Slight variations in the sample produce different hash values of the sample data. The answer linked below indicates that enough different samples might produce an exhaustive set of hash values.

The following fingerprint hash system was proposed: Fingerprint hash I am trying to determine whether or not the number of samples required is infeasibly large or small enough to be feasible.

Hashing mathematical models of a fingerprint patterns seems to provide a sufficient solution. A mathematical model of a fingerprint would focus only on the key distinguishing features of the fingerprint pattern and thus ignore other differences between a pair of images.

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    @polcott The number of hashes needed depends on the variability of human fingerprints, the hardware characteristics of the scanner and the ratio of false positive and false negatives allowed. It's impossible for us to make this estimate for you. Also, some humans do not have fingerprints.
    – A. Hersean
    May 19, 2021 at 16:27
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    You've switched "enough" for "exhaustive", but it's the same problem: exhaustive for what? I think what you want to ask is "what is the minimum viable number of samples to positively identify someone?"
    – schroeder ♦
    May 19, 2021 at 17:57
  • The comment above still holds after your edit: no one can give you a general case. Different fingerprint readers read inputs differently. At best, someone might give you an answer about feasibility for a given reader. I've seen extremely high-resolution scanners that map out the patterns on the ridges of a fingerprint. You only need one sample from that reader.
    – schroeder ♦
    May 19, 2021 at 17:59
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    We have, and you are dismissing our responses. Please consider that we know what we are talking about. The linked item talks about fingerprint identification as a concept. You are asking about implementation. Once you jump that gap, there are other issues to consider. So, as we've been saying all along, there can only be an answer, or even a range, for a given reader and reader algorithm.
    – schroeder ♦
    May 19, 2021 at 18:19
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    Any readers -- no. Any algorithms is one of the most unlimitedly-difficult questions one can ask. 😉 It's almost inevitable that one exists, but whether one is currently known is unlikely. It would take a lot of man-hours to find it, certainly (if even reasonably possible).
    – JamesTheAwesomeDude
    May 19, 2021 at 18:39

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I am going for possibly feasible, or definitely infeasible. If ten samples might be enough we have an answer. If less than a million will never be enough then we have an answer.

Put this down as definitely infeasible, then (at least unless you come up with a very accurate, extremely lossy, very clever mathematical "flattening" of the fingerprint scans.)

Fingerprint scanning is an analog process: it's essentially a (potentially very poor quality) photograph; according to some website, these may reasonably be as low as 96×96 pixels.

If we take the coarse assumptions that each of these pixels can be reduced to a bit depth of around 3 (that is, around 8 possible brightness levels), that 95% of a 96×96px scan's pixels are fixed by a finger (or fix-able by your mathematical analysis), and that the finger will only move up to ±10px in each of the X and Z axes, that gives you approximately too many possible images that a given fingerprint might produce.

If you want to find a way to hash "fingerprints", you will have to find a serious analytic reduction of them based on pivotal attributes, and go about hashing that mathematical characterization of each instead.

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  • Comments are not for extended discussion; this conversation has been moved to chat.
    – Rory Alsop ♦
    May 20, 2021 at 11:10
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As the prior answer indicates it is definitely infeasible to hash actual fingerprint data so that an exhaustive set of hash values is a feasibly small number. On the other hand, hashing a mathematical model of a fingerprint pattern may provide a sufficient solution.

A mathematical model of a fingerprint would focus only on the key distinguishing features of the fingerprint pattern and thus ignore other differences between a pair of images.

Mathematical Models of Fingerprints

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    "During minutiae-based matching, the set of minutiae are extracted from the two fingerprints and stored as sets of points in the two dimensional plane...minutiae-matching is most widely used approach in fingerprint recognition ..." -- all fingerprint scanners extract a mathematical model of the fingerprint. The image isn't stored, if that's what you were thinking. So, I'm not sure if this is an "answer" to the problem. That paper is about adding more data points to avoid errors and speed up the matching process.
    – schroeder ♦
    May 19, 2021 at 22:48
  • @schroeder Because mathematical models of fingerprints screen out an enormous amount of irrelevant differences between two different fingerprint images this would seem to be a reliable way for biometric authentication to store fingerprint data in a cryptographically secure environment. It may still be susceptible to an evil maid attack on the client side. It would be at least as secure as using credit card numbers over the internet.
    – polcott
    May 19, 2021 at 23:03
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    I'm saying that that is what is happening currently. John Deter's answer in the linked post assumes mathematical models... This "answer" adds nothing. It's just a discovery of yours for how the process works.
    – schroeder ♦
    May 20, 2021 at 6:43

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