A complicated calculus-based anti-spam CAPTCHA

Filed Under: Spam

Eggheads at the Ruđer Bošković Institute in Zagreb, Croatia, are having some geeky fun with their web forms.

If you want to login to the institute's Quantum Random Bit Generator service, you will be asked the usual questions like your username and password, but then you'll be faced by a mathematical problem that may give you a nighmarish memories of your schooldays doing advanced calculus.

Complicated calculus-based anti-spam CAPTCHA

Hmm.. it's a bit more complicated than the typical sort of CAPTCHA used by websites around the world to try to block spam bots and automated systems:


Sometimes, of course, these randomly-generated CAPTCHAs can go very wrong - potentially causing unintended offense to some amusement.

Somehow I don't think the calculus-based CAPTCHA is going to catch on with the general public.

Hat-tip: Los Angeles Times via The Register.

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29 Responses to A complicated calculus-based anti-spam CAPTCHA

  1. I'm sure I've seen similar CAPTCHAs ages ago. (Though never "in the wild".) More complicated ones too. This one isn't too difficult. And having people solve a CAPTCHA like this before allowing them to leave comments on your website, may keep the vast majority of daft comments at bay!

    • Miguel · 1669 days ago

      "This one isn't too difficult"
      That's your opinion; for me it is impossible to solve.

      "And having people solve a CAPTCHA like this before allowing them to leave comments on your website, may keep the vast majority of daft comments at bay!"
      Don't be so sure.

  2. aaa · 1669 days ago

    Since when have researchers or scientists been replaced with eggheads? What does that make a consultant like you?

  3. Aleksejs · 1669 days ago

    Mashup with WolframAlpha anyone? ;)

  4. Andreas · 1669 days ago

    As far as I can see, the differentiation always gives (1 or 0)*prefaktor [see sin/cos(pi/2)]. Thus by reading just a part of the equation, without any other operation than MUL, the solution can be found.

    This is much easier to be solved than google's scanned words.

  5. ccsccs7 · 1669 days ago

    I think this is to keep the nosey average Internet user from wasting resources they know nothing about.

    • Andreas · 1669 days ago

      I agree. These captchas aren't to protect against bots, but to protect against people who obviously dont need quantum random numbers.

    • Guest · 1669 days ago

      Agreed. For a site where the intended user would almost certainly know basic calculus, this is a great idea.

    • Mark F. · 1189 days ago

      Why didn't someone think of this earlier? Necessary and a non-issue for users of the site.

  6. Asian Kid · 1669 days ago

    It would be hard if a child visited the site. Like me, I'm only 11 years old and I don't know anything about calculus. Does this mean I'm a spam bot because I don't know calculus?

    • Richard · 1669 days ago

      Why would anyone who didn't know calculus need to generate a quantum random bit?

      Even if you don't know calculus, there are plenty of tools you can use to solve this equation. For example:

    • Guest · 1669 days ago

      I don't think this site is intended for the average child. Those gifted children who might be visiting the site for a legitimate purpose would likely be able to solve the calculus questions. Those who can't solve the question probably are not the intended users of the site.

      Some of the captcha questions on this particular site are actually no harder than the skill testing questions one might find on a bag of chips. For example, this is what I got on just one reload of the page: -1 + (-2) + 3 - (-1) - 0 + (-3) + 3 = ?

  7. John · 1669 days ago

    So would someone post the answer please? ;)

  8. Hermes · 1669 days ago


  9. Mrs. W. · 1669 days ago

    I love this idea.

    Obviously, it doesn't make sense for the average person who may never take a calculus class, but for those of us who wish to keep our skills sharp, it would be great to be able to select this type of captcha. I used to do math tournaments, but I haven't had a math class (apart from stats) in over ten years and I'm terribly rusty.

    Even a simple browser add-on that gated every 10th or 20th page with a math problem would be awesome. Someone please get on this. :)

  10. On some pages I see that they provide the answer on the page itself. Like psst the answer is: so and so.

    On other pages require to copy and paste a particular text.

    While others use the captcha as 1+1=?

    BTW, what is quantum number?

  11. Biscuit-Rascal · 1669 days ago

    They're just "showing off" --- asking a question about PARTIAL derivatives, when they're using a function of only one variable. The answer is -36.

  12. Tinned_Tuna · 1669 days ago

    I agree with Biscuit-Rascal, I calculate -36, but I will have to crack out my old calculus book to see if I've done it correctly.

  13. svcghost · 1669 days ago

    Signing up is simple and free! All you need is a keyboard and a calculator!

  14. stevenschaaf · 1669 days ago

    -36, although I did it in my head....I've been wrong in the past and it's 1am

  15. James · 1664 days ago

    The obvious answer must be 42.

  16. mackman · 1664 days ago

    36 ? how in the world do you get 36? I got 42

    • CHS Math teacher · 1663 days ago

      Derivative of cos=-sin,
      use the chain rule derivative of inside is 6
      therefore equals 6(-sin(6x+pi/2))(6)
      simplify -36sin(6x+pi/2)
      evaluate at 2pi = -36(1) = -36

      • David · 1090 days ago

        You missed the "The Hitchhiker's Guide to the Galaxy" reference.

        42 is the "Answer to the Ultimate Question of Life, the Universe, and Everything"

  17. KeithBa · 1663 days ago

    I had to reload the page twice before I could solve it. Personally, I like the mathematical Captchas and far from sieving the desirable commenters, it would just have someone use their mind before they post (something many people do not).

  18. roy jones jr · 1659 days ago

    It is a nice prototype idea. Putting mathemical captchas (sans the calculus ones) is a good way to have structured comment blogs & forums. They should also use them for downloads.

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About the author

Graham Cluley runs his own award-winning computer security blog at https://grahamcluley.com, and is a veteran of the anti-virus industry having worked for a number of security companies since the early 1990s. Now an independent security analyst, he regularly makes media appearances and gives computer security presentations. Follow him on Twitter at @gcluley