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Sep 8, 2014 at 18:03 comment added MattyW I think I've satisfied myself that the question doesn't make any sense. The question comes down to if you have a $\mathrm{verify}f$ that you know the implementation of. But even though you know the implementation it's impossible to work out what value you can give it to make it return true
Sep 8, 2014 at 17:59 comment added MattyW I'm explaining myself badly. Specifically it's a question about security - but without certificates or keys. Let's say I have a server that you send numbers to and it gives you numbers back. I give you the code for contacting the server and verifying that you contacted my server. In this code you can change the url but not the verify function. You can implement your own server that still passes the existing verification function because by just examining the verify function you can work out when it will return true for any given input
Sep 8, 2014 at 17:25 comment added David Richerby Perhaps we're using "implementation" in different ways. To me, the implementation is, essentially, the algorithm used to compute $f$. Knowing that the function $\mathrm{verify}f$ exists doesn't tell you how to find it and it certainly doesn't tell you what code I wrote to implement the function defined by $f$.
Sep 8, 2014 at 17:17 comment added MattyW But if $\mathrm{verify}f$ contains a verification that the value returned by $f$ contains a prime number with $x$ numbers (for example) you can work out that's what the implementation of $f$ does.
Sep 8, 2014 at 16:49 history answered David Richerby CC BY-SA 3.0