CAPTCHA as a Communications Problem

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CAPTCHA as a Communications Problem

• By Kunjan Rana
• EC517

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What Is a CAPTCHA?

• Completely
• Automated
• Public
• Turing test to tell
• Computers and
• Humans
• Apart

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Purpose of CAPTCHAs

• Automated process for determining whether an
  internet form submission is completed by a
  legitimate human user or a malicious bot
• Most common form is a visual CAPTCHA (in image)

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Motivation

• Almost every major web application uses a visual
  CAPTCHA
• Many visual CAPTCHAs are easily crackable, since
  there is currently no analytical method for
  studying the limits of detection for various
  CAPTCHA schemes

Easy to crack! ?
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Though the Lens of IT
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Immediate Consequences of the new methodology

• Easier to visualize problem of detection
  Increase the amount of computation necessary on
  the detector side, but make the increases of
  computation trivial for human detectors (increase
  alphabet of Y by increasing alphabet of X and/or
  increasing channel distortion possibilities)

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Evolution of CAPTCHAs
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Some CAPTCHAs have features that reduce
randomization

• Examples
• Limiting the variations of letters to english
  words decreases entropy of the source since it is
  no longer a uniform distribution of the letters

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Some CAPTCHAs are very difficult for humans to
detect
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Some CAPTCHAs are impossible for humans to detect

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What can the capacity of this channel tell us?

• A capacity equal to log X for this channel
  would show that all output from the channel is
  potentially decodable by a human observer
• Programmer can design distortions based upon this
  measure
• However, humans are sub-optimal decoders, so this
  does NOT tell us if humans can decode the image

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How can we find it?

• We can find the capacity (albeit inefficiently)
  using its definition
• Then, we can observe overlapping outputs

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Geometric Distortions

• For the purposes of this project, I focused on
  warping transformations

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Method

• Take fixed alphabet W for input and generate a
  single 8x8 image corresponding to each
  (generating X)

A B C D
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Find all possible transformations

• Find a mapping between the old coordinate system
  (x1,y1) to the new one (x2,y2)

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Dealing with non-integer (x2,y2)

• Distribute the original values intensity among
  neighboring points
• Example given 2x2 grid and shift of x of 0.25
  and shift of y of 0.75

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Result

• The system achieved capacity for up to 2 pixels
  moved in each direction (although this does not
  mean that the other cases were distinguishable
  for a human observer)

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Too much work for a simple answer!

• Number of computations become exponentially large
  as size of image and bounds on distortion grow.

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Other limitations of model

• This system treats the input and output as a
  one-channel-use problem. In reality, many OCRs
  segment the image into individual letters. So, W
  can be modeled as a random process with a smaller
  alphabet.
• Also, some distortion systems (channels) have
  knowledge of their input, and will bound the
  amount of distortion based upon this information

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Future Directions

• Treatment of geometric distortions as time-warped
  data, or correlations between inputs
• Quantization of values and power limitation of
  the pixel intensity